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:
Maximum height is 64 feet achieved by the ball.
Step-by-step 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.
