What Are Quadratic Functions

In algebra, quadratic functions are any form of the equation y ax2   bx   c, where a  is not equal to 0, which can be used to solve complex math equations that attempt to evaluate missing factors in the equation by plotting them on a u-shaped figure called a parabola.  The graphs of quadratic functions are parabolas; they tend to look like a smile or a frown. Points Within a Parabola The points on a graph represent possible solutions to the equation based on high and low points on the parabola. The minimum and maximum points can be used in tandem with known numbers and variables to average the other points on the graph into one solution for each missing variable in the above formula. When to Use a Quadratic Function Quadratic functions can be highly useful when trying to solve any number of problems involving measurements or quantities with unknown variables. One example would be if you were a rancher with a limited length of fencing and you wanted to fence in two equal-sized sections creating the largest square footage possible. You would use a quadratic equation to plot the longest and shortest of the two different sizes of fence sections and use the median number from those points on a graph to determine the appropriate length for each of the missing variables. Eight Characteristics of Quadratic Formulas Regardless of what the quadratic function is expressing, whether it be a positive or negative parabolic curve, every quadratic formula shares eight core characteristics. y  Ã‚  ax2  Ã‚  bx  Ã‚  c, where  a  is not equal to 0The graph this creates is a parabola -- a u-shaped figure.The parabola will open upward or downward.A parabola that opens upward contains a vertex that is a minimum point; a  parabola that opens downward contains a vertex that is a maximum point.The domain of a quadratic function consists entirely of real numbers.If the vertex is a minimum, the range is all real numbers greater than or equal to  the  y-value. If the vertex is a maximum, the range is all real numbers less than or equal to the  y-value.An axis of symmetry (also known as a line of symmetry) will divide the parabola into mirror images. The line of symmetry is always a vertical line of the form x n, where n is a real number, and its axis of symmetry is the vertical line x 0.The x-intercepts are the points at which a parabola intersects the x-axis. These points are also known as zeroes, roots, solutions, and solution sets. Each quadratic function will have two, one, or no x-intercepts. By identifying and understanding these core concepts related to quadratic functions, you can use quadratic equations to solve a variety of real-life problems with missing variables and a range of possible solutions.

The Role of the Watch in William Faulkners A Rose for Emily

The Role of the Watch in William Faulkners A Rose for Emily Even the casual reader of William Faulkner will recognize the element of time as a crucial one in much of the writers work, and the critical attention given to the subject of time in Faulkner most certainly fills many pages of criticism. A goodly number of those pages of criticism deal with the well-known short story, A Rose for Emily. Several scholars, most notably Paul McGlynn, have worked to untangle the confusing chronology of this work (461-62). Others have given a variety of symbolic and psychological reasons for Emily Griersons inability (or refusal) to acknowledge the passage of time. Yet in all of this careful literary analysis, no one has discussed one†¦show more content†¦She resists change because for her change will alw ays involve loss. She must prevent time from passing if she is to hold on to what matters to her. Her desire to keep her life from changing is further evidenced by her reluctance to have her fathers body removed and buried and by her refusal to a llow str eet numbers to be attached to the door of her beloved family home. The extreme example of her need to control change, to keep time in her pocket, is her poisoning Homer and placing him carefully in the upstairs room. The townspeople have joined forces with the representatives of her own family and are on the verge o f separating her from him, just as earlier they separated her from her father. Homer alive and active in her life has become too serious an affront to those around her. The only way she can keep him with her is to arrest his activity and to suspend his vi tality. As a corpse, this Yankee outsider will be less offensive to the sensibilities of the closed Southern community. (Evidence exists of the towns complicity in Homers murder. Their knowledge of Emilys purchase of the arsenic, followed by Homer Barrons disappearance and the subsequent odor surrounding the Grierson house indicate at least some level of community awareness of what had happened.) More important for Emily, however, Homer will now stay fixed as a part of her life forever. The consequence of Emilys attempt to keep things from changing is that time for her loses itsShow MoreRelatedEssay on Oh Who Will Protect Poor Emily?1027 Words   |  5 PagesIn Faulkner’s â€Å"A Rose for Emily†, there is a constant theme of protection for Emily Grierson, because she was a woman living in the south after the civil war and the requirements that were placed on women enable to be honorable. That is to say that, women needed to be protected by the men of the community during that time in history and women’s actions were constantly under watch to see if a woman was honorable and worthy of protection or not. Within the story, there are many instances in which thisRead MoreWilliam Faulkner s Writing Style1486 Words   |  6 PagesWilliam Faulkner, who lived his entire live in Mississippi, was a Nobel Prize- winning writer who became well-known for his work set in the American South. After dropping out of high school and working in multiple different fields, he was commissioned as a major in the Hawaiian Territorial Forces. Faulkner later enrolled in the University of Mississippi and began his writing career; writer Sherwood Anderson gave Faulkner advice, stating that he should write about his native home of Mississippi. Read MoreThe Search for Time in Yoknapatawpha County1908 Words   |  8 Pagesyear and the time period of the story. Furthermore, in the short story â€Å"A Rose for Emily† by William Faulkner, the setting is a source of conflict. The narrator’s of the story, the town’s people, have an unknown entity, but because the story shifts between time periods and settings, the reader acquires different points of view from the same conflict. The theme of tradition and change in the short story â€Å"A Rose for Emily†, is enhanced by time, the southern gothic literature, and the post Civil WarRead MoreAnalysis of the Short Story A Rose for Emily Essay1038 Words   |  5 PagesThe reason I c hose to analyze â€Å"A Rose for Emily† by William Faulkner is because I am a lover of suspense and terror. The story totally caught my attention because the general tone is one of violence, gloom, and terror. The setting also plays an important role because it gives the reader a better understanding of the different situations. The main character, Emily, plays the role of a tragic figure that seems to be seen only from the outside. Sometimes people judge others from the outside, but theyRead MoreWilliam Faulkners A Rose for Emily1600 Words   |  7 Pages William Faulkners A Rose for Emily  is set in the small southern town of Jefferson during the early decades of the twentieth century . At this time, vast and cardinal changes were being made by the upcoming new south to conceal and move from the horrid truths that were a part of the towns history. In lieu of this, Jefferson was at a turning point in which they were having difficulty coming to terms with these cha nges . Integrating Faulkners use of character and symbols with other sourcesRead MoreLiterary Elements in A Rose For Emily Essay1695 Words   |  7 PagesEscaping Loneliness In A Rose for Emily, William Faulkners use of setting and characterization foreshadows and builds up to the climax of the story. His use of metaphors prepares the reader for the bittersweet ending. A theme of respectability and the loss of, is threaded throughout the story. Appropriately, the story begins with death, flashes back to the past and hints towards the demise of a woman and the traditions of the past she personifies. Faulkner has carefully crafted a multi-layeredRead MoreRose for Emily1559 Words   |  7 PagesEscaping Loneliness In A Rose for Emily, William Faulkners use of setting and characterization foreshadows and builds up to the climax of the story. His use of metaphors prepares the reader for the bittersweet ending. A theme of respectability and the loss of, is threaded throughout the story. Appropriately, the story begins with death, flashes back to the past and hints towards the demise of a woman and the traditions of the past she personifies. Faulkner has carefully crafted a multi-layeredRead More The Nature of Time and Change in William Faulkners A Rose for Emily1763 Words   |  8 PagesThe Nature of Time and Change in William Faulkners A Rose for Emily In A Rose for Emily, William Faulkners use of language foreshadows and builds up to the climax of the story. His choice of words is descriptive, tying resoundingly into the theme through which Miss Emily Grierson threads, herself emblematic of the effects of time and the nature of the old and the new. Appropriately, the story begins with death, flashes back to the near distant past and leads on to the demise of a woman andRead More Role of Women in Hemmingways Hills like White Elephants, Lawrences The Horse Dealers Daughter and2273 Words   |  10 PagesRole of Women in Hemmingways Hills like White Elephants, Lawrences The Horse Dealers Daughter and Faulkners A Rose for Emily The role of women in society is constantly questioned and for centuries women have struggled to find their place in a world that is predominantly male oriented. Literature provides a window into the lives, thoughts and actions of women during certain periods of time in a fictitious form, yet often truthful in many ways. Ernest Hemmingways Hills like White ElephantsRead MoreAnalysis of A Rose for Emily, by William Faulkner and The Yellow Wallpaper, by Charlotte Perkins Gilman2621 Words   |  11 Pages In the short stories â€Å"A Rose for Emily† written by William Faulkner and â€Å"The Yellow Wallpaper†Ã¢â‚¬  written by Charlotte Perkins Gilman, the protagonists experience mental illness, loneliness, feelings of being in control of their lives, and feelings of being insane. Both main characters struggle against male domination and control. The two stories take place in the late 1800’s - early 1900’s, a time where men’s place in society was supe rior to that of women. Each story was written from a different

Walking Groups

Question: Write an article onillustrating the benefits of walking groups for the individuals with poor health. Answer: The article deals in illustrating the benefits of walking groups for the individuals with poor health. The article helps in understanding the socio-economic indicators in order to understand the barriers that could hamper with the involvement of the individuals with the walking. The authors have implemented the qualitative approach in order to make the readers better understand about the benefits of walking groups being facilitated by the photo elicitation process. The article has been able to determine both the positive and negative aspects of the individual experiences related to the exercises referral scheme. While, walking groups has been able to influence most of the individuals to participate in the healthier activities, a few of them do not like socializing (Hanson et al., 2016). Thus, the authors have illustrated about an exercise referral scheme that could be effective in engaging new walkers from the disadvantage groups into walking interventions. Authors Argument The authors, in their article, have illustrated on the grim fact that people consider gym, medical attention, and other modern and expensive techniques, to be useful in healing their serious ailments. The people have a tendency to join the group with the expectation of earning an experience, which however, has no close connection with the thought of improving the health conditions. To belong, and to become a part of the group of the other fellow beings, is a significant factor that motivates the people. However, after joining the social group, these individuals realize the benefits related with the physical activity of walking. Critique The most important point in the writing that immediately strikes a reader is the lack of awareness among the public regarding the benefits of walking. The journal clearly shows how a huge number of people were unaware and absolutely ignorant about the benefit of walking. According to Nutsword et al., (2013), the casual approach and indifference to walking could not be more striking, when an interviewee reported bluntly that he usually does not go out for a walk. His I pad, TV, luxurious house are providing him with all the necessary happiness and comfort he requires in life. The writer not only talks of walking as an important physical activity that should be appreciated, but he also emphasizes the importance of the same, for mental bliss. According to Mitchell et al., (2013), group walking, in an alienated, tech-obsessed world, turns out to be an activity that promoted socialization with other fellow beings, deep interaction with nature, and a source of refreshment and amusement for the walkers. One of the most unique and commendable aspects of the journal is that the writer focuses more on the mental health benefits of walking. Group walking helps in promoting mental health, by curing clinical depression, stress, hypertension, isolation and sleeplessness. The writer reminds the reader that it is important to go out of the door, explore the natural beauty of the beach, park, promenade, interact with nature, and to socialize with people of various classes. Suggestion The article lacks the illustration of the various theories related to the health behavior and health behavior change based on the characteristics of the individuals. According to Nutbeam Harris, (2004), the theory of health behavior helps in illustrating on the best practice interventions on the self-regulation skills and abilities of the individuals, which could help in improving the health conditions. The theory of health behavior utilizes the Social cognitive Theory, and hence examines and exploits the inter-relation between the environment and the human beings. Thus, the article should have been more effective to make the readers understand the health behavior of the individuals in a better way. Conclusion The article discusses about the importance of walking which could be useful in healing their serious ailments. The article has been able to determine both the positive and negative aspects of the individual experiences related to the exercises referral scheme. In this regard, group walking is required to be appreciated for the individuals to enjoy health benefits. It should be considered as an implication, which is participated in a social group requiring the mingling of people in the society. This process in the due course, help in refreshing the minds of the individuals. The participation in the process would itself enable the individuals to understand the physical health benefits where they could themselves would feel the motivation to continue participating on their own. Those who joined, admiring the idea of leisure walking, became aware of their own level of physical fitness, in comparison with that of the crowd, and could accordingly take steps to improve their physical health . References Astell-Burt, T., Mitchell, R. Hartig, T., (2014). The association between green space and mental health varies across the lifecourse. A longitudinal study. Journal of epidemiology and community health, 68(6), pp.578-583.Fry, D. Zask, A., (2016). Applying the Ottawa Charter to inform health promotion programme design. Health promotion international, p.daw022.Grembowski, D., (2015). The practice of health program evaluation. Sage Publications.Hanson, S., Guell, C. Jones, A., (2016). Walking groups in socioeconomically deprived communities: A qualitative study using photo elicitation. Health place, 39, pp.26-33.Mitchell, R., (2013). Is physical activity in natural environments better for mental health than physical activity in other environments?. Social Science Medicine, 91, pp.130-134.Nutbeam, D., Harris, E. (2004). Theories on health behaviour and health behaviour change: individual characteristics. Theory in a nutshell.Nutsford, D., Pearson, A.L. Kingham, S., (2013). An ecolo gical study investigating the association between access to urban green space and mental health. Public health, 127(11), pp.1005-1011.

Antioxidant Activity of Mangrove free essay sample

All forms of life maintain a reducing environment within their cells. This reducing environment is preserved by enzymes that maintain the reduced state through a constant input of metabolic energy. Disturbances in this normal redox state can cause toxic effects through the production of peroxides and free radicals that damage all components of the cell, including proteins,  lipids, and  DNA. Oxidative stress occurs when free radicals, which are not neutralized by antioxidants, go on create more volatile free radicals and damage cell walls, vessel walls, proteins, fats and even the nucleus of our cells. A free radical or reactive species is any chemical species capable of independent existence possessing one or more unpaired electrons. Biological free radicals are thus highly unstable molecules that have electrons available to react with various organic substrates. The reactive species generally include ROS and RNS, though reactive chlorine species also part of the reactive species. Reactive oxygen species  (ROS) are chemically reactive molecules containing oxygen. Examples include  oxygen  ions  and  peroxides. ROS form as a natural byproduct of the normal metabolism of  oxygen  and have important roles in  cell signaling  and  homeostasis. Normally, cells defend themselves against ROS damage with  enzymes  such as  alpha-1-microglobulin,  superoxide dismutase,  catalases,  lactoperoxidase, glutathione peroxidase  and  peroxiredoxins. Small molecule antioxidants such as  ascorbic acid  (vitamin C),  tocopherol  (vitamin E),  uric acid, and  glutathione also play important roles as cellular antioxidants. Reactive Nitrogen Species (RNS)  are radical nitrogen-based molecules that can act to facilitate nitrosylation reactions. Reactive Nitrogen Species (RNS) include nitrous oxide, peroxynitrate, nitrosyl cation, nitrous acid, etc. Many free radicals are the result of naturally occurring processes such as oxygen metabolism and inflammatory processes. For example, when cells use oxygen to generate energy, free radicals are created as a consequence of ATP production by the mitochondria. Exercise can increase the levels of free radicals as can environmental stimuli such as ionizing radiation (from industry, sun exposure, cosmic rays, and medical X-rays), environmental toxins, altered atmospheric conditions (e.g. , ozone and nitrous oxide (primarily from automobile exhaust). Lifestyle stressors such as cigarette smoking and excessive alcohol consumption are also known to affect levels of free radicals. Some of the important reactive species are superoxide (O2. –), shydrogen peroxide (H2O2), hydroxyl radicals (OH. ), nitric oxide (NO. ), etc. An extensive, highly effective group of protective agents and defense mechanisms referred to collectively as the  Antioxidant Defense System  (ADS), acts to regulate oxidative reactions. There are two types of antioxidant systems i. e.enzymatic and non enzymatic antioxidant system develop in plants. Enzymatic system includes superoxide dismutase, glutathione peroxidase, glutathione reductase, catalases, etc. These form the body’s endogenous defense mechanisms to help protect against free radical-induced cell damage. They require micronutrient cofactors such as  selenium, iron, copper, zinc, and manganese for their activity. Non-enzymatic system include such as  ascorbic acid  (Vitamin C), polyphenols  ,  tocopherols, etc. Vitamin C is the most important water-soluble antioxidant in extracellular fluids. Vitamin C helps to neutralize ROS in the water or aqueous phase before it can attack the lipids. Vitamin E is the most important lipid soluble antioxidant. It is important as the chain-breaking antioxidant within the cell membrane. It can protect the membrane fatty acids from lipid peroxidation. Vitamin C in addition is capable of regenerating vitamin E. Beta carotene and other carotenoids also have antioxidant properties. In human, some of the notable diseases caused due to oxidative stress include heart disease is the leading cause of death worldwide. Heart disease risk is raised by several factors including high  cholesterol  levels,  high blood pressure, cigarette smoking, and  diabetes (Sundararajan et al. , 2006; Tawaha et al. , 2007; Nanasombat and Teckchuen, 2009). These promote  atherosclerosis. Atherosclerosis refers to formation of hardened walls of the arteries that impairs blood flow to the heart and other vital organs. Cancer kills millions worldwide. Diet may be the cause for cancer in as much as 35% of all human cancers. Low antioxidant intake in diet may also be responsible. Low dietary intake of fruits and vegetables doubles the risk of most types of cancers. Pro-oxidants, or those who generate free radicals, stimulate cell division and these form the beginnings of mutagenesis and tumor formation. When a cell with a damaged DNA strand divides, it gives rise to disturbed and deformed clusters of cells that form the cancer. In addition, cigarette smoking and chronic inflammation lead to strong free radical generation that seems to be the reason for many cancers. The respiratory system is a well known target for free radical insult. This comes from endogenous factors as well as exposure to air pollutants and toxins, cigarette smoke etc. Recent studies suggest that free radicals may be involved in the development of pulmonary disorders such as  asthma. Antioxidants have been seen to reduce the development of asthmatic symptoms. Vitamin C, vitamin E, and  beta carotene supplementation has been associated with improved lung function. Free radicals can also damage nerves and the  brain. Formation of  cataracts  is believed to involve damage to lens protein by free radicals. This leads to opacity of the lens. Cataract  formation may be slowed with the regular consumption of supplemental antioxidants like vitamin E, vitamin C, and the carotenoids. Other diseases like Diabetes, Rheumatoid  arthritis  etc. are also associated with low antioxidant levels in blood. Several standard established antioxidant drugs such as butylhydroxytoluene (BHT) and rutin have been reported to be toxic to living cells (Madhavi et al, 1995, Bursal amp; Gulcin, 2011, Gocer et al, 2011). BHT drugs are known to be the most prevalent and approved antioxidant scavengers worldwide, have equally been reported to be toxic to the lungs, even at a lower concentration. As oxidative stress causes many human diseases, the use of natural antioxidants is intensively studied. Antioxidants are widely used in  dietary supplements  and have been investigated for the prevention of diseases such as cancer,  coronary heart disease  and even  altitude sickness. Plant contains a variety of phytochemical such as phenols, steroids, tannins, saponins, carbohydrates, etc having antioxidant activity that can be used for the removal of human diseases caused due to the oxidative stress. As part of their adaptation from marine life, terrestrial plants develop antioxidant system producing different phytochemicals such as  ascorbic acid  , polyphenols  and  tocopherols having antioxidant property. Mangrove plants are found to have medicinal values and have been used traditionally by local medical practitioners in worldwide. In nature, more than 65 species of mangrove plants, 18 species are found to be widely used by local medical practitioners in many countries like Africa, South East Asia, South America and Australia. These 12 species viz. Acanthus clicifolius, Aegiceras majus, Avicennia africana, A. marina, A. officinalis, Ceriops caudolleana, Exocoecaria agallocha, Kandelia rhecdi, Nypa fruticans, Rhizophora mangle, R. mcronata and Sonneratia caseolaris are used to cure some deeded diseases like leprosy, elephantiasis, tuberculosis, malaria, dysentery, ulcers and some skin diseases. Balsco et al,1976 and Banerjee and Gosh,1998 reported that 27 out of 65 species of mangrove are present in India respectively. The mangroves are the coastal tropical forest; grow in the intertidal deltaic areas, having higher salt concentration. Some species such as the Grey Mangrove can also tolerate the storage of large amounts of salt in their leaves – which are discarded when the salt load is too high. Mangroves can also restrict the opening of their stomata. This allows the mangrove to conserve its fresh water, ability vital to its survival in a saline environment. Mangroves are able to turn their leaves to reduce the surface area of the leaf exposed to the hot sun. This enables them to reduce water loss through evaporation. A distinctive feature of mangroves is their far-reaching, exposed roots. While these roots come in many different shapes and sizes, they all perform an important function – structural support in the soft soils. Some species of mangroves have pneumataphores, which are above-ground roots. These are filled with spongy tissue and peppered with small holes that offer structural support and allow oxygen to be transferred to the roots trapped below ground in the anaerobic (low oxygen) soils. The roots of many mangrove species are also adapted to stop the intake of a lot of the salt from the water before it reaches the plant. Some mangrove species have evolved to produce seeds that float. The tide acts as the method of dispersal to avoid crowding of young plants. Other mangrove species are viviparous. They retain their seeds until after it has germinated and a long, cylindrical propagule has formed. When it has matured to this stage, the parent tree drops it into the water, where it remains dormant until it finds the soil and is able to put out roots. Referring to the facts cited above the present study was designed with the following objectives. OBJECTIVES Selection of mangrove plants for antioxidant activity on the basis of their ethenomedicinal importance. 2. Preparation of mangrove plant extracts by successive extraction methods. 3. Phytochemical evaluation of the mangrove plant extracts. 4. Evaluation of antioxidant activity following in vitro assay techniques. Normally free radical formation is controlled naturally by various beneficial compounds known as antioxidants. When there is deficiency of these antioxidants damage due to free radicals can become cumulative and debilitating. Antioxidants are capable of stabilizing, or deactivating, free radicals before they attack cells. Some of the important reactive species and their biological effects are superoxide anion, hydrogen peroxide, peroxynitrite, hydroxyl radicals, etc. The free radical superoxide is generated from O2 by multiple pathways. They can be summarized into following categories, such as: i) NADPH oxidation by NADPH oxidase; ii) oxidation of xanthine or hypoxanthine by xanthine oxidase; iii) oxidation of reducing equivalents (e. g., nicotinamide adenine dinucleotide [reduced NADH], NADPH, and FADH2 [FAD reduced]) via the mitochondrial electron transport system; iv) autoxidation of monamines (e. g. , dopamine, epinephrine, and norepinephrine), flavins, and hemoglobin in the presence of trace amounts of transition metals; v) one-electron reduction of O2 by cytochrome P-450. Superoxide anion (O2-) is a reactive oxygen species that reacts quickly with nitric oxide (NO) in the vasculature. The reaction p roduces peroxynitrite and depletes the bioactivity of NO. This is important because NO is a key mediator in many important vascular functions including regulation of smooth muscle tone and blood pressure, platelet activation, and vascular cell signaling (Guzik et al, 2002). Peroxynitrite itself is a highly reactive species which can directly react with various biological targets and components of the cell including lipids, thiols, amino acid residues, DNA bases, and low-molecular weight antioxidants (ODonnell et al, 1999). Peroxynitrite can react directly with proteins that contain transition metal centers. Therefore, it can modify proteins such as hemoglobin, myoglobin, and cytochrone c by oxidizing ferrous heme into its corresponding ferric forms. Peroxynitrite may also be able to change protein structure through the reaction with various amino acids in the peptide chain. Hydrogen peroxide (H2O2) is a two-electron reduction state, formed by dismutation of †¢O2- or by direct reduction of O2. It is lipid soluble and thus able to diffuse across membranes. Hydrogen peroxide and superoxide radical (O2. –) by themselves are relatively less damaging, but they can form species such as hydroxyl radicals.