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Chapter 11: Q . 11.37TI (page 1099)

Find the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.

Short Answer

Expert verified

The equation isy=-120(x-20)2+20

Step by step solution

01

Given information

Given the base is40ftwide and20fthigh

02

Calculate the vertex 

Let the lower left side of the bridge be the origin of the coordinate grid at the point

Since the base is 40feet wide the point (40,0)represents the lower right side.

The bridge is 20feet high at the highest point. The highest point is the vertex of the parabola so the y-coordinate of the vertex will be 20

So the vertex is(20,20)

.
03

Substitute in standard form and form the equation

Substituting, we get

y=a(x-h)2+ky=a(x-20)2+200=a(0-20)2+20400a=-20a=-120

The equation isy=-120(x-20)2+10

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