SOLUTION: A cannon fires a cannonball whose path is a parabola with vertex at the highest point of the path. If the cannonball lands 1600 feet from the cannon and the highest point reac

Question 688908: A cannon fires a cannonball whose path is a parabola with vertex
at the highest point of the path. If the cannonball lands 1600 feet from the
cannon and the highest point reached is 3200 feet above the ground, find an
equation for the path of the cannonball.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You can relate 2 variables- plotted on
the vertical axis, and plotted on the horizontal
axis. I know that the 2 roots of the equation are:

This is because is where the cannonball is
fired from and is where it lands.
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The general form for a parabola is

You are given 2 points, ( 0,0 ) and ( 1600, 0 )
(0,0)

So now the equation looks like

-------------------
(1600,0)

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The vertex is at

You are given that

Since

and

The equation is:

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check answer:
Does it go through (0,0)?

OK
Does it go through (1600,0)?

OK
Is the vertex at ( 800, 3200 )?