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Chapter 11: Q. 11.38TI (page 1100)

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=-15(x-5)2+5

Step by step solution

01

Given information

Given the base is 10ft wide and 5ft high

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 10feet wide the point (10,0)represents the lower right side.

The bridge is 5feet high at the highest point. The highest point is the vertex of the parabola so the ycoordinate of the vertex will be 5

So the vertex is(5,5)

03

Step 3:Substitute in standard form and form the equation

Calculating, we get

y=a(x-h)2+ky=a(x-5)2+50=a(0-5)2+525a=-5a=-15

The equation isy=-15(x-5)2+5

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