# Quadratic Problem Help

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• December 28th 2009, 09:22 AM
andi01
Quadratic Problem Help
Thanks for your help in advance, here's the problem:

The path of a golf ball can be modeled by a quadratic equation. The path of a ball hit an angle of 10 degrees can be modeled by h=-0.002d^2+0.4d where h is the height in meters and d is the horizontal distance the ball travels in meters until it first hits the gorund.

a) What is the maximum height reached by the ball?

The answer is 20m, usually I would just sub in 0 for d to find h but in this case it's different. What should I do?
• December 28th 2009, 12:41 PM
Soroban
Hello, andi01!

Quote:

The path of a golf ball can be modeled by a quadratic equation.
The path of a ball hit an angle of 10° can be modeled by: $h\:=\:-0.002d^2+0.4d$
where $h$ is the height in meters and $d$ is the horizontal distance.

a) What is the maximum height reached by the ball?

The answer is 20m.
Usually I would just sub in 0 for d to find h. . . Why?

Think of what you said . . .

You let $d = 0$.
The ball has not moved yet.
What is its height?
. . Obviously it's still on the ground!

Here's one way of looking at it:

The graph of $h \:=\:-0.002d^2 + 0.4d$ is a down-opening parabola: $\cap$

Its maximum is at its vertex.
The vertex is at: . $v \:=\:\frac{\text{-}b}{2a} \quad\Rightarrow\quad d \:=\:\frac{\text{-}0.4}{2(\text{-}0.002)} \:=\:100$

The maximum height is: . $h \:=\:-0.002(100^2) + 0.4(100) \:=\:20$ m.

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