4. The path of a golf ball can be modeled by $h = - 0.002 d^{2} + 0.4 d$ , where $h$ is the height in meters and $d$ is the horizontal distance the ball travels,
Show an algebraic solution for full marks.
b) What is the horizontal distance of the ball from the golfer when the ball reaches its
5. The height of a ball is shown in the provided graph. Answer the following. a). Determine the person's initial height when they threw the ball. (1)
b). Determine how long the ball in the air.
c). Determine the maximum height of the ball.
d). Determine how high the ball was after 3 seconds. 1
e). Determine how long it took the ball to return to the same height it was thrown from. 2
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The horizontal distance of the ball from the golfer when the ball reaches its maximum height is $100$ meters

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Step 1 ： $h = - 0.002 d^{2} + 0.4 d$

Step 2 ：To find the horizontal distance when the ball reaches its maximum height, we need to find the vertex of the parabola. The vertex occurs at $d = \frac{- b}{2 a}$ , where $a = - 0.002$ and $b = 0.4$

Step 3 ： $d = \frac{- 0.4}{2 (- 0.002)}$

Step 4 ： $d = \frac{- 0.4}{- 0.004}$

Step 5 ： $d = 100$

Step 6 ：The horizontal distance of the ball from the golfer when the ball reaches its maximum height is $100$ meters

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