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!!PLEASE HELP!!

The path of a baseball is modeled by the equation
y=-0.25x^(2) +4x+3 where x represents the time (in seconds) and y represents the height of the baseball.
- Find and interpret the y-intercept. Find the maximum height of the baseball. Then sketch a graph of the path.

(please provide steps on how to solve if you can)

User Nimish Goel
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1 Answer

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8 votes

Answer:

The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.

Explanation:

The $y$-intercept is $-1$. The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$. Here is a sketch of the path.

From the $y$-intercept, we see that the baseball starts at height $y=-1$. It reaches a maximum height at $x=\ln(4)$; that is, $y=0$. From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.

User Marty Chang
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