We're sorry, this computer has been flagged for suspicious activity.
If you are a member, we ask that you confirm your identity by entering in your email.
You will then be sent a link via email to verify your account.
If you are not a member or are having any other problems, please contact customer support.
Thank you for your cooperation
Sciencing_Icons_Science SCIENCE
Sciencing_icons_biology biology, sciencing_icons_cells cells, sciencing_icons_molecular molecular, sciencing_icons_microorganisms microorganisms, sciencing_icons_genetics genetics, sciencing_icons_human body human body, sciencing_icons_ecology ecology, sciencing_icons_chemistry chemistry, sciencing_icons_atomic & molecular structure atomic & molecular structure, sciencing_icons_bonds bonds, sciencing_icons_reactions reactions, sciencing_icons_stoichiometry stoichiometry, sciencing_icons_solutions solutions, sciencing_icons_acids & bases acids & bases, sciencing_icons_thermodynamics thermodynamics, sciencing_icons_organic chemistry organic chemistry, sciencing_icons_physics physics, sciencing_icons_fundamentals-physics fundamentals, sciencing_icons_electronics electronics, sciencing_icons_waves waves, sciencing_icons_energy energy, sciencing_icons_fluid fluid, sciencing_icons_astronomy astronomy, sciencing_icons_geology geology, sciencing_icons_fundamentals-geology fundamentals, sciencing_icons_minerals & rocks minerals & rocks, sciencing_icons_earth scructure earth structure, sciencing_icons_fossils fossils, sciencing_icons_natural disasters natural disasters, sciencing_icons_nature nature, sciencing_icons_ecosystems ecosystems, sciencing_icons_environment environment, sciencing_icons_insects insects, sciencing_icons_plants & mushrooms plants & mushrooms, sciencing_icons_animals animals, sciencing_icons_math math, sciencing_icons_arithmetic arithmetic, sciencing_icons_addition & subtraction addition & subtraction, sciencing_icons_multiplication & division multiplication & division, sciencing_icons_decimals decimals, sciencing_icons_fractions fractions, sciencing_icons_conversions conversions, sciencing_icons_algebra algebra, sciencing_icons_working with units working with units, sciencing_icons_equations & expressions equations & expressions, sciencing_icons_ratios & proportions ratios & proportions, sciencing_icons_inequalities inequalities, sciencing_icons_exponents & logarithms exponents & logarithms, sciencing_icons_factorization factorization, sciencing_icons_functions functions, sciencing_icons_linear equations linear equations, sciencing_icons_graphs graphs, sciencing_icons_quadratics quadratics, sciencing_icons_polynomials polynomials, sciencing_icons_geometry geometry, sciencing_icons_fundamentals-geometry fundamentals, sciencing_icons_cartesian cartesian, sciencing_icons_circles circles, sciencing_icons_solids solids, sciencing_icons_trigonometry trigonometry, sciencing_icons_probability-statistics probability & statistics, sciencing_icons_mean-median-mode mean/median/mode, sciencing_icons_independent-dependent variables independent/dependent variables, sciencing_icons_deviation deviation, sciencing_icons_correlation correlation, sciencing_icons_sampling sampling, sciencing_icons_distributions distributions, sciencing_icons_probability probability, sciencing_icons_calculus calculus, sciencing_icons_differentiation-integration differentiation/integration, sciencing_icons_application application, sciencing_icons_projects projects, sciencing_icons_news news.
- Share Tweet Email Print
- Home ⋅
- Math ⋅
- Algebra ⋅
Everyday Examples of Situations to Apply Quadratic Equations
10 Ways Simultaneous Equations Can Be Used in Everyday Life
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0. The letter X represents an unknown, and a b and c being the coefficients representing known numbers and the letter a is not equal to zero.
Calculating Room Areas
People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side. For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x times 2x, or 2x^2. This equation must be less than or equal to four to successfully make a box using these constraints.
Figuring a Profit
Sometimes calculating a business profit requires using a quadratic function. If you want to sell something – even something as simple as lemonade – you need to decide how many items to produce so that you'll make a profit. Let's say, for example, that you're selling glasses of lemonade, and you want to make 12 glasses. You know, however, that you'll sell a different number of glasses depending on how you set your price. At $100 per glass, you're not likely to sell any, but at $0.01 per glass, you'll probably sell 12 glasses in less than a minute. So, to decide where to set your price, use P as a variable. You've estimated the demand for glasses of lemonade to be at 12 - P. Your revenue, therefore, will be the price times the number of glasses sold: P times 12 minus P, or 12P - P^2. Using however much your lemonade costs to produce, you can set this equation equal to that amount and choose a price from there.
Quadratics in Athletics
In athletic events that involve throwing objects like the shot put, balls or javelin, quadratic equations become highly useful. For example, you throw a ball into the air and have your friend catch it, but you want to give her the precise time it will take the ball to arrive. Use the velocity equation, which calculates the height of the ball based on a parabolic or quadratic equation. Begin by throwing the ball at 3 meters, where your hands are. Also assume that you can throw the ball upward at 14 meters per second, and that the earth's gravity is reducing the ball's speed at a rate of 5 meters per second squared. From this, we can calculate the height, h, using the variable t for time, in the form of h = 3 + 14t - 5t^2. If your friend's hands are also at 3 meters in height, how many seconds will it take the ball to reach her? To answer this, set the equation equal to 3 = h, and solve for t. The answer is approximately 2.8 seconds.
Finding a Speed
Quadratic equations are also useful in calculating speeds. Avid kayakers, for example, use quadratic equations to estimate their speed when going up and down a river. Assume a kayaker is going up a river, and the river moves at 2 km per hour. If he goes upstream against the current at 15 km, and the trip takes him 3 hours to go there and return, remember that time = distance divided by speed, let v = the kayak's speed relative to land, and let x = the kayak's speed in the water. While traveling upstream, the kayak's speed is v = x - 2 -- subtract 2 for the resistance from the river current-- and while going downstream, the kayak's speed is v = x + 2. The total time is equal to 3 hours, which is equal to the time going upstream plus the time going downstream, and both distances are 15km. Using our equations, we know that 3 hours = 15 / (x - 2) + 15 / (x + 2). Once this is expanded algebraically, we get 3x^2 - 30x -12 = 0. Solving for x, we know that the kayaker moved his kayak at a speed of 10.39 km per hour.
Related Articles
10 ways simultaneous equations can be used in everyday..., how are linear equations used in everyday life, how to find a distance from velocity & time, how to calculate the velocity of an object dropped..., how to calculate probability with percentages, how to use algebra 2 in real life, how do the laws of motion apply to basketball, the use of mathematics in everyday life, how to calculate the distance, rate and time, how to calculate tangential force, how do i use the factors in math activities in real..., how to solve probability questions, how to calculate force from velocity, sports fan vs. data scientist: how to fill out an ncaa..., how to solve a time in flight for a projectile problem, how to calculate tangential speed, how to calculate load force, how to calculate time-weighted averages, how to find acceleration in g's.
- Math is Fun: Real World Examples of Quadratic Equations
About the Author
Kevin Wandrei has written extensively on higher education. His work has been published with Kaplan, Textbooks.com, and Shmoop, Inc., among others. He is currently pursuing a Master of Public Administration at Cornell University.
Find Your Next Great Science Fair Project! GO
We Have More Great Sciencing Articles!
How to Calculate the Velocity of an Object Dropped Based on Height
How are quadratic equations used in solving real-life problems and making decisions?
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
Step-by-step explanation:
New questions in Math
Article Categories
Book categories, collections.
- Academics & The Arts Articles
- Math Articles
- Algebra Articles
Applying Quadratics to Real-Life Situations
Algebra ii all-in-one for dummies.
Sign up for the Dummies Beta Program to try Dummies' newest way to learn.
Quadratic equations lend themselves to modeling situations that happen in real life, such as the rise and fall of profits from selling goods, the decrease and increase in the amount of time it takes to run a mile based on your age, and so on.
The wonderful part of having something that can be modeled by a quadratic is that you can easily solve the equation when set equal to zero and predict the patterns in the function values.
The vertex and x -intercepts are especially useful. These intercepts tell you where numbers change from positive to negative or negative to positive, so you know, for instance, where the ground is located in a physics problem or when you’d start making a profit or losing money in a business venture.
The vertex tells you where you can find the absolute maximum or minimum cost, profit, speed, height, time, or whatever you’re modeling.
Sample question
In 1972, you could buy a Mercury Comet for about $3,200. Cars can depreciate in value pretty quickly, but a 1972 Comet in pristine condition may be worth a lot of money to a collector today.
Let the value of one of these Comets be modeled by the quadratic function v ( t ) = 18.75 t 2 – 450 t + 3,200, where t is the number of years since 1972. When is the value of the function equal to 0 (what is an x -intercept), what was the car’s lowest value, and what was its value in 2010?
The car’s value never dropped to 0, the lowest value was $500, and the car was worth $13,175 in the year 2010. In this model, the y -intercept represents the initial value. When t = 0, the function is v (0) = 3,200, which corresponds to the purchase price.
Find the x -intercepts by solving 18.75 t 2 –450 t + 3,200 = 0. Using the quadratic formula (you could try factoring, but it’s a bit of a challenge and, as it turns out, the equation doesn’t factor), you get –37,500 under the radical in the formula. You can’t get a real-number solution, so the graph has no x -intercept. The value of the Comet doesn’t ever get down to 0.
Find the lowest value by determining the vertex. Using the formula,
This coordinate tells you that 12 years from the beginning (1984 — add 12 to 1972), the value of the Comet is at its lowest. Replace the t ’s in the formula with 12, and you get v (12) = 18.75(12) 2 – 450(12) + 3,200 = 500.
The Comet was worth $500 in 1984. To find the value of the car in 2010, you let t = 38, because the year 2010 is 38 years after 1972. The value of the car in 2010 is v (38) = 18.75(38) 2 – 450(38) + 3,200 = $13,175.
Practice questions
The height of a ball t seconds after it’s thrown into the air from the top of a building can be modeled by h ( t ) = –16 t 2 + 48 t + 64, where h ( t ) is height in feet. How high is the building, how high does the ball rise before starting to drop downward, and after how many seconds does the ball hit the ground?
The profit function telling Georgio how much money he will net for producing and selling x specialty umbrellas is given by P ( x ) = –0.00405 x 2 + 8.15 x – 100.
What is Georgio’s loss if he doesn’t sell any of the umbrellas he produces, how many umbrellas does he have to sell to break even, and how many does he have to sell to earn the greatest possible profit?
Chip ran through a maze in less than a minute the first time he tried. His times got better for a while with each new try, but then his times got worse (he took longer) due to fatigue.
The amount of time Chip took to run through the maze on the a th try can be modeled by T ( a ) = 0.5 a 2 – 9 a + 48.5. How long did Chip take to run the maze the first time, and what was his best time?
A highway underpass is parabolic in shape. If the curve of the underpass can be modeled by h ( x ) = 50 – 0.02 x 2 , where x and h ( x ) are in feet, then how high is the highest point of the underpass, and how wide is it?
Following are answers to the practice questions:
The building is 64 feet tall, the ball peaks at 100 feet, and it takes 4 seconds to hit the ground.
The ball is thrown from the top of the building, so you want the height of the ball when t = 0. This number is the initial t value (the y -intercept). When t = 0, h = 64, so the building is 64 feet high.
The ball is at its highest at the vertex of the parabola. Calculating the t value, you get that the vertex occurs where t = 1.5 seconds. Substituting t = 1.5 into the formula, you get that h = 100 feet.
The ball hits the ground when h = 0. Solving –16 t 2 + 48 t + 64 = 0, you factor to get –16( t – 4)( t + 1) = 0. The solution t = 4 tells you when the ball hits the ground.
The t = –1 represents going backward in time, or in this case, where the ball would have started if it had been launched from the ground — not the top of a building.
Georgio loses $100 (earns –$100) if he sells 0, needs to sell 13 to break even, and can maximize profits if he sells 1,006 umbrellas.
If Georgio sells no umbrellas, then x = 0, and he makes a negative profit (loss) of $100. The break-even point comes when the profit changes from negative to positive, at an x -intercept. Using the quadratic formula, you get two intercepts: at x = 2,000 and x is approximately 12.35.
The first (smaller) x -intercept is where the function changes from negative to positive. The second is where the profit becomes a loss again (too many umbrellas, too much overtime?). So, 13 umbrellas would yield a positive profit — he’d break even (have zero profit).
The maximum profit occurs at the vertex. Using the formula for the x -value of the vertex, you get that x is approximately 1,006.17. Substituting 1,006 into the formula, you get 4,000.1542; then substituting 1,007 into the formula, you get 4,000.15155.
You see that Georgio gets slightly more profit with 1,006 umbrellas, but that fraction of a cent doesn’t mean much. He’d still make about $4,000.
Chip took 40 seconds the first time; his best time was 8 seconds.
Because the variable a represents the number of the attempt, find T (1) for the time of the first attempt. T (1) = 40 seconds. The best (minimum) time is at the vertex. Solving for the a value (which is the number of the attempt),
He had the best time on the ninth attempt, and T (9) = 8.
The underpass is 50 feet high and 100 feet wide.
The highest point occurs at the vertex:
The x -coordinate of the vertex is 0, so the vertex is also the y -intercept, at (0, 50). The two x -intercepts represent the endpoints of the width of the overpass. Setting 50 – 0.02 x 2 equal to 0, you solve for x and get x = 50, –50. These two points are 100 units apart — the width of the underpass.
About This Article
This article can be found in the category:.
- Applying the Distributive Property: Algebra Practice Questions
- Converting Improper and Mixed Fractions: Algebra Practice Questions
- How to Calculate Limits with Algebra
- Understanding the Vocabulary of Algebra
- Understanding Algebraic Variables
- View All Articles From Category
- How it works
- Homework answers
Answer to Question #85317 in Math for Janet
Quadratic equations lend themselves to modeling situations that happen in real life and in decision making, such as the rise and fall of profits from selling goods, the decrease and increase in the amount of time it takes to run a mile based on your age, and so on.
The wonderful part of having something that can be modeled by a quadratic is that you can easily solve the equation when set equal to zero and predict the patterns in the function values.
https://www.dummies.com/education/math/algebra/applying-quadratics-to-real-life-situations/
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS !
Leave a comment
Ask your question, related questions.
- 1. Which of the following statements true or false? Give a short proof or a counter example in support
- 2. A distribution system has the following constraints: Factory A B C Capacity (in units): 45 15 40
- 3. A sales manager wishes to assign four sales territories to four salespersons. The salespersons diffe
- 4. A distribution system has the following constraints: Factory: A B C Capacity(in units): 45 15 40
- 5. Which of the following statements are true or false? Give a short proof or a counter example in supp
- 6. sin inverse( xsquare /y) is a homogeneous function of x and y.True or false?
- 7. A company owns two flour mills viz. A and B, which have different production capacities for high,med
- Programming
- Engineering
Who Can Help Me with My Assignment
There are three certainties in this world: Death, Taxes and Homework Assignments. No matter where you study, and no matter…
How to Finish Assignments When You Can’t
Crunch time is coming, deadlines need to be met, essays need to be submitted, and tests should be studied for.…
How to Effectively Study for a Math Test
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
IMAGES
VIDEO
COMMENTS
Quadratic equations govern many real world situations such as throwing a ball, calculating certain prices, construction, certain motions and electronics. They are most often used to describe motion of some sort.
According to Math Is Fun, real-world examples of the quadratic equation in use can be found in a variety of situations, from throwing a ball to riding a bike. In each example, the predictive qualities of the quadratic equation can be used t...
The most common use of the quadratic equation in real world situations is in the aiming of missiles and other artillery by military forces. Parabolas are also used in business, engineering and physics.
So, what are quadratic equations used for? Quadratic equations are used in many real-life situations such as calculating the areas of an
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed
Answer: Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the
When solving word problems requiring quadratic equations, the first and most important step is to translate the word problem into a quadratic equation. Then we
There are many real-world situations that deal with quadratics and parabolas. Throwing a ball, shooting a cannon, diving from a platform and
Answer: In daily life we use quadratic formula as for calculating areas, determining a product's profit or formulating the speed of an object. In addition
Quadratic equations have many applications in daily life because they are crucial to human survival. ... Quadratic equations must be used directly
Another common use of the quadratic equation in real world applications is to find maximum (the most or highest) or minimum (the least or lowest) values of
Quadratic equations lend themselves to modeling situations that happen in real life, such as the rise and fall of profits from selling goods
Quadratic equations lend themselves to modeling situations that happen in real life and in decision making, such as the rise and fall of
judgments that are used as reference material in deciding to solve a problem.