Quadratic Functions from Situations Practice

Question

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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.