You throw a ball straight up from a rooftop. The ball misses the rooftop on its

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:

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

Question 12 options:

y = -16x2 + 80x + 50

y = -16x2 + 100x + 30

y = -10x2 + 60x + 64

y = -12x2 + 80x + 46

x, seconds after ball is thrown y, ball's height, in feet, above the ground 1 114 2 146 4 114

Explanation / Answer

y=ax2+bx+c

(1,114)

114=a+b+c

(2,146)

146=4a+2b+c

(4,114)

114=16a+4b+c

So we have three equations which are

a+b+c=114 , 4a+2b+c =146 , 16a+4b+c=114

Solving them we will get a=-16, b=80, c=50

So the required equation is

y=-16x2+80x +50

Correct option is the first option .

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