Question

Ellie hit a tennis ball into the air. the path of the ball can be modeled by y=-x^2+8x+2 where y represents the height in feet of the ball x seconds after it is hit into the air. what is the maximum height of the ball?

Answer 1

18 ft

Explanation:

You want to know the maximum height of a ball whose height is modeled as a function of time (x) by the equation y = -x² +8x +2.

Vertex form

The vertex of this downward-opening parabola will be the point at which the height is a maximum. We can rearrange the equation to vertex form:

y = -(x² -8x) +2 . . . . . . group variable terms, factor out leading coefficient

y = -(x² -8x +16) +2 +16 . . . . . add and subtract the square of half the x-coefficient

y = -(x -4)² +18 . . . . . . vertex form

Comparing this to the generic vertex form ...

y = a(x -h)² +k . . . . . . . parabola with vertex (h, k)

we see that the vertex of the given equation is ...

(h, k) = (4, 18)

The maximum height of the ball is 18 feet.