Question

1. The height of a bridge is given by y--3r? + I, where y is the height of the bridge (in miles) and x is the number ofmiles from the base of the bridge.a. How far from the base of the bridge doesb. What is the maximum height of the bridge?the maximum height occur?

Answer 1

we have

y=-3x^2+x

this is a quadratic equation (vertical parabola open dwnward)

The vertex is a maximum

Convert the eqaution in vertex form

so

y=a(x-h)^2+k

where

(h,k) is the vertex

y=-3x^2+x

Factor -3

y=-3(x^2-1/3)

Complete the square

y-1/12=-3(x^2-1/3+1/36)

rewrite as perfect squares

y-1/12=-3(x-1/6)^2

y=-3(x-1/6)^2+1/12 ------> equation in vertex form

the vertex is the point (1/6,1/12)

therefore

The maximum height of the brige is 1/12 miles and occur at 1/6 miles from the base of the bridge