Question

Sara kicked a football. The height of the ball (in meters above the ground) ttt seconds after Sara kicked it is modeled by h(t)=-5t^2+20th(t)=−5t 2 +20th, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 20, t Sara wants to know the height of the ball above the ground at its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) At its highest point, how far above the ground was the ball? meters

Answer 1

Answer:

$h(t) = -5(t-2)^2+20$

20 meters

Step-by-step explanation:

Answer 2

The vertex form of the equation is h(t) = -5(t-2)^2 - 4 and the ball was 20 meters above the ground

Vertex form of an expression

The standard vertex form of a quadratic equation is expressed as (a-h)^2 + k

Given the height of the ball (in meters above the ground) t seconds after Sara kicked it is modelled by h(t)=-5t^2+20t

Write in vertex form

h(t)=-5t^2+20t

h(t) = -5(t^2 - 4t)
h(t) = -5(t^2 - 4t + 2^2) - 2^2
h(t) = -5(t-2)^2 - 4

Hence the vertex form of the equation is h(t) = -5(t-2)^2 - 4

At the highest point t = -b/2a
t = -20/2(-5)
t = -20/-10
t = 2ssecs

Substitute t = 2 into the function

h(2) = -5(2)^2 + 20(2)
h(2) = -20 + 40
h(2) = 20 meters

Hence the ball was 20 meters above the ground

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