Question

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?

Answer 1

Answer:

Step-by-step explanation:

Given that:

• Spans = 80ft

• Maximum height = 20ft

As we know that the Parabola is of type :

$(x - x_{0}) ^{2}$ = -4a(y -$y_{0}$ ) where: $x_{0} y_{0}$ is the origin of the line so we have:

$x_{0} = 0$ and $y_{0} = 20$

<=> $x^{2}$ = -4a(y-20)

at y = 0, we have:

$x^{2}$ = -4a(0-20)

<=> $x^{2} = 80a$

<=> x = ±$\sqrt{80a}$

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

40 = $\sqrt{80a}$

<=> 1600 = 80a

<=> a = 20

The equation for the parabola is: $x^{2} = 80(y-20)$

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