Question

ja’von kicks a soccer ball into the air. the function f(x)=-16(x-2)^2+64 represents the height of the ball,in feet, as a function of time, x, in seconds. what is the maximum height the ball reaches

Answer 1

Hello from MrBillDoesMath!

Answer:

Max height= 64 feet

Discussion:

A negative number times a positive or zero valued number is <=0. So

-16(x-2)^2 <=0, then

f(x) = -16(x-2)^2 + 64 <= 0 + 64

so the max of f(x) is 64 feet and is reached when -16(x-2)^2 = 0. That is when x = 2.

Thank you,

MrB

Answer 2

Maximum height is 64 feet achieved by the ball.

Explanation:

Ja'von kicks a ball into the air. Function f(x) = - 16(x - 2)² + 64 represents the height of the ball in feet as a function of time x in seconds.

As the function is a parabola and equation is in the vertex form f(x) = - a(x - h)² + k, vertex of the parabola will be (h, k)

Therefore, vertex of the given function f(x) = -16(x - 2)² + 64 will be (2, 64).

Now in the given equation coefficient "a" starts with negative notation so opening of the parabola will be downwards.

Since opening of the parabola is downwards then vertex will be the highest point after the kick.

So after 2 seconds of the kick value of the function will represent the value of maximum height achieved by the ball.

f(2) = -16(2-2)² + 64 = 64 feet

Therefore, 64 feet is the maximum height the ball will reach.