If an arch is in the shape of a parabola and it spans 80 ft with a maximum height of 20 feet what is the equation for the parabola and what is it's height from the center?

Step-by-step explanation:

Given that:

As we know that the Parabola is of type :

= -4a(y - ) where: is the origin of the line so we have:

and

<=> = -4a(y-20)

at y = 0, we have:

= -4a(0-20)

<=>

<=> x = ±

But we know that 2x= 80 <=> x= 40, so:

40 =

<=> 1600 = 80a

<=> a = 20

The equation for the parabola is:

It's height from the center at x= 0 => y= 20

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