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Sharon hits a golf ball off the ground. The function [tex]\( h \)[/tex] represents the height of the golf ball, in feet, [tex]\( t \)[/tex] seconds after it is hit.
[tex]\[ h(t) = -16(t-3)^2 + 144 \][/tex]

Which of the following statements describes this situation correctly?

A. The golf ball will be on the ground at 0 and 16 seconds.
B. The golf ball will be on the ground at 3 and 6 seconds.
C. The golf ball will be on the ground at 0 and 3 seconds.
D. The golf ball will be on the ground at 0 and 6 seconds.



Answer :

GinnyAnswer
To determine the times at which the golf ball will be on the ground, we need to find the values of [tex]\( t \)[/tex] for which [tex]\( h(t) = 0 \)[/tex]. The height function provided is:

[tex]\[ h(t) = -16(t-3)^2 + 144 \][/tex]

Step-by-step solution:

1. Set the height function equal to zero:

[tex]\[ 0 = -16(t-3)^2 + 144 \][/tex]

2. Isolate the quadratic term:

[tex]\[ 16(t-3)^2 = 144 \][/tex]

3. Divide both sides by 16:

[tex]\[ (t-3)^2 = \frac{144}{16} \][/tex]
[tex]\[ (t-3)^2 = 9 \][/tex]

4. Take the square root of both sides:

[tex]\[ t-3 = \pm3 \][/tex]

5. Solve for [tex]\( t \)[/tex] by adding 3 to both solutions:

[tex]\[ t - 3 = 3 \quad \text{or} \quad t - 3 = -3 \][/tex]
[tex]\[ t = 3 + 3 \quad \text{or} \quad t = 3 - 3 \][/tex]
[tex]\[ t = 6 \quad \text{or} \quad t = 0 \][/tex]

Thus, the golf ball will be on the ground at [tex]\( t = 0 \)[/tex] seconds and [tex]\( t = 6 \)[/tex] seconds.

The correct statement is:
- The golf ball will be on the ground at 0 and 6 seconds.