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AfilCa [17]
3 years ago
15

A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equ

als the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Mathematics
1 answer:
Ierofanga [76]3 years ago
6 0

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Evaluate the function y= -3 (1/4) for x =-3 on top of the 1/4 is where the x goes. so it is 1/4 x
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\text{Consider the function}\\
\\
y=-3\left ( \frac{1}{4} \right )^x\\
\\
\text{now to evaluate the value of the function at }x=-3, \text{ we substitute}\\
x=-3 \text{ in the given function and solve further for y.}\\
\\
\text{so we get}\\
\\
y=-3\left ( \frac{1}{4} \right )^{-3}\\
\\
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\\
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