Question

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. Consider the following data:
x, seconds after ball is thrown | y, ball's height in feet, above the ground

1 | 114
2 | 146
4 | 114



Find the quadratic function y = ax2 +bx + c whose graph passes through the given points.

Answer 1

A. y = -12x2 + 80x + 46

B. y = -10x2 + 60x + 64

C. y = -16x2 + 100x + 30

D. y = -16x2 + 80x + 50

Answer 2

I think it is D but I'm not sure.

Answer 3

Well, I'm hopping back and forth, so Ive only taken a brief look. Usually these formulas start with a -16x^2 just from experience xD I haven't though much so the one thing I do notice is that since this is parabolic, everything will be symmetric about the vertex. Now the vertex is -b/2a. Now I also notice that 1 and 4 have the same value, which means the vertex HAS to be in between 1 and 4. The middle of 1 and 4 is 2.5. So what this means is that -b/2a has to equal 2.5. Only two of your answers meet that condition, a and d.

Answer 4

Now between a and d, you would just need to plug in values. f(1) should equal 114.

Answer 5

Looks like they do for a and d. Now to check f(2).

Answer 6

Looks like only d works for f(2), so your answer is d : )

Answer 7

Thank you!

Answer 8

Yep, np ^_^