Question

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amir stands on a balcony and throws a ball to his dog, who is at ground level.
the balls height (in meters above the ground), ( x ) seconds after amir threw it, is modeled by:
( h(x) = -(x - 2)^2 + 16 )
how many seconds after being thrown will the ball hit the ground?
seconds
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Explanation:

Step1: Set height to 0

When the ball hits the ground, its height \( h(x) = 0 \). So we set up the equation:
\( 0 = -(x - 2)^2 + 16 \)

Step2: Solve for \( x \)

First, rewrite the equation as:
\( (x - 2)^2 = 16 \)
Take the square root of both sides:
\( x - 2 = \pm 4 \)

Case 1: \( x - 2 = 4 \)

Solve for \( x \):
\( x = 4 + 2 = 6 \)

Case 2: \( x - 2 = -4 \)

Solve for \( x \):
\( x = -4 + 2 = -2 \)

Since time cannot be negative, we discard \( x = -2 \).

Answer:

6