Copyright

Using Quadratic Functions to Model a Given Data Set or Situation

Using Quadratic Functions to Model a Given Data Set or Situation
Coming up next: Terminology of Polynomial Functions

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:01 Quadratic Functions
  • 0:59 Modeling
  • 1:56 A Data Set
  • 3:38 A Situation
  • 4:49 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how quadratic functions are used to model situations and data gathered from real world scenarios. See how our function fits our data and situation well.

Quadratic Functions

Quadratic functions are those functions with a degree of 2. What this means is that they will have, at most, three terms, and the highest exponent is always a 2. Yes, quadratic functions will always have the term with the exponent of 2.

The general or standard form of all quadratic functions is f(x) = ax^2 + bx + c, where a, b, and c are your coefficients, and x is your variable. Your coefficients can be any number. If a coefficient is 0, then it makes that term disappear. For quadratic functions, though, because the ax^2 term always needs to be present, the coefficient of a cannot be 0.

Your variable, x, can be any letter that is convenient for the function. If we are talking about time, our variable can be t. If we are talking about height, then our variable can be h. Our variable can be any letter that makes our function easy to understand.

Modeling

Of course, you come across these functions in math problems and tests and exams. But these functions also appear in the real world as models of real life events. For example, and this is just one example, the path an object, such as a baseball, travels after its been hit follows this quadratic function:


quadratic modeling


Where g is 4.9 for meters and 16 for feet, v sub 0 is our initial velocity, and h sub 0 is our initial height. Our coefficient g comes from the force of gravity and has been calculated specific to Earth.

Our initial velocity is the speed the object is traveling upwards at when released, and our initial height is the height at which our object is released. Our function then gives the height of the object at any given time. Let's take a closer look at modeling using this quadratic function.

A Data Set

We can be given a data set, a collection of data points, to consider. Since we are dealing with a falling object after it is released, we will look at data points that follow the path of a falling object, such as a human cannonball. Say we are given the following data points:

time (s) height (m)
0 3
1 14.8
2 16.8
3 9

We are told that these data points follow the path of a human cannonball under the force of gravity on Earth. We already know what the quadratic function looks like. So, we just need to find the initial velocity, the initial height, and whether we are dealing in meters or feet.

We look at our data points and see that at time 0, our human cannonball was at a height of 3. That means that our initial height is 3 meters. Since we are dealing in meters, our g is 4.9. To find our initial velocity, then, we can use our second data point, (1, 14.8).

We plug in these values into our quadratic function for the movement of an object under gravity. We get 14.8 = - 4.9 * 1^2 + v sub 0 * 1 + 3. This turns into 14.8 = -4.9 + v sub 0 + 3. Adding like terms, we get 14.8 = -1.9 + v sub 0.

Solving for v sub 0 by adding 1.9 to both sides gives us an initial velocity of 16.7 meters per second. Okay, we have all the information we need to build our quadratic function. Plugging in all our necessary items, we get this for the quadratic function that models this set of data:


quadratic modeling


To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support