You throw a ball straight up from a rooftop.

Question

​x, seconds after the ball is thrown	​y, ball's​ height, in​ feet, above the ground​
​1	354
3	266
4	174

You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the​ ball's height above the​ ground, y, after x seconds.

Find the quadratic function

y=ax2+bx+c

whose graph passes through the given points.

Answer 1

1. a + b + c = 354
2. 9a + 3b + c = 266
3. 16a + 4b + c = 174

We can perform Gaussian elimination on the left side's (3x3) coefficient matrix augmented with a vertical vector (3 x 1) representing the vector of the right sides of these equations..

Or we can set up a Matrix A, of the left side's (3x3) coefficients, multiply by it by x = (a, b, c)^T s.t. Ax = (354, 266, 174)^T then we left multiply both sides of this equation by A^-1 , the inverse of A, and we get

x = A^-1(354, 266, 174)^T so x = (a, b, c)^T = (-16, 20, 350)^T

So our equation is:

y = -16x^2 + 20x + 350

Finally, check for reasonableness.