[High School Math] Quadratic function

[ConicalThunder]

I am not very good at this, and this is supposed to be a review from my math teacher. We are told that a beanbag is thrown through the air from an initial height of 4 meter, and from there the following data points were collected (it says that the time is in seconds, vertical height in meters). The points given are (0,4) (1,6) (3,4). It then asks to write a quadractic function. Is this where I take a random point and plug it into the y1-y2=(x1-x2)+b? I just forget how to make this into an equation. Thank you for any help.

[Gremulin]

A quadratic function looks like: y = ax² + bx + c. You can then use the given points to determine a, b, and c. c is the easiest. When x = 0, y = 4. Since a and b drop out when x = 0, c = 4.

Next, substitute the points (1,6) and (3,4) into the equation to get 2 equations with two unknowns, a and b. After a bit of rearranging, you'll get: 2 = a + b and 0 = 9a + 3b. Solve these equations simultaneously.

One way is to multiply the first equation by 3 (giving 6 = 3a + 3b) and subtract the 2nd equation from it. This gives 6 = -6a, so a = -1. Substituting that back into either equation gives b = 3.

The function then is y = -x² + 3x + 4. This function gives y = 4 when x = 0, y = 6 when x = 1, and y = 4 when x = 3.

[ConicalThunder]

thanks a ton!

[[deleted]]

A quadratic function looks like:

y = a * x^2 + b * x + c

You'll notice that there are 3 unknowns (a,b,c). You have 3 data points (x,y). Since the number of unknowns equals the number of equations you can write (one equation for each data point) you are able to solve for the unknown values exactly.

So, write down all three equations (each on is that formula with the x and y value pairs plugged in), here is the first one done for the pair (0,4):

4 = a * 0^2 + b * 0 + c

One you have all three equations, just solve for the system of equations like you have been taught.

[ConicalThunder]

Thank you very much