Question

Quadratic Functions from Situations Practice
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Question
A football player kicks the ball with an initial upward velocity of 60 feet per second. This situation is modeled using the equation h=−16t2+60t+0
, where h is the height in feet and t is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth.(1 point)
feet
Remaining Attempts : 3
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Answer 1

To find the maximum height the football will reach, we can use the vertex formula for a quadratic function, which is given by \( t = -\frac{b}{2a} \) for the equation in the standard form \( h = at^2 + bt + c \).

In your case, the equation is:

\[ h = -16t^2 + 60t + 0 \]

Here, \( a = -16 \) and \( b = 60 \).

1. Calculate the time at which the maximum height occurs:

\[
t = -\frac{b}{2a} = -\frac{60}{2(-16)} = -\frac{60}{-32} = \frac{60}{32} = 1.875 \text{ seconds}
\]

2. Next, substitute \( t = 1.875 \) back into the height equation to find the maximum height:

\[
h = -16(1.875)^2 + 60(1.875) + 0
\]

Calculating \( (1.875)^2 \):

\[
(1.875)^2 = 3.515625
\]

Now substituting:

\[
h = -16(3.515625) + 60(1.875)
\]
\[
h = -56.25 + 112.5
\]
\[
h = 56.25
\]

Thus, the maximum height the football will reach is **56.25 feet**.