# Question #d2356

##### 1 Answer

#### Answer:

Equation of coaster's path:

Height of the peak:

#### Explanation:

[Although this was asked under Geometry:Right-Angled Triangle, my tools were strictly Algebraic. I anyone has a Geometric solution I would like to see it posted here.]

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Measuring (in feet) the horizontal distance from the peak as the x-coordinate and the distance above ground as the y-coordinate:

The coaster will pass through

The vertex of its path will occur at

The general vertex form of a parabola is:

for a parabola with vertex at

Therefore the coaster's path must be modeled by

and

So the coaster's parabolic path equation is

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If

when