Posted by **Sophie** on Tuesday, October 25, 2011 at 5:24pm.

An engineer is desingning a parabloic arch, the arch must be 15 m high , and 6 m wide, at a height of 8 m

a) determine a quadratic fundtion that satisfies these conditions

b) what is the width of the arch at its base

- Math -
**Steve**, Wednesday, October 26, 2011 at 4:42am
Let the arch be centered on the y-axis. Then the equation will be

y = -ax^2 + k

It will have height 6 at x = 3 and -3

The vertex will be at (0,15)

y = -ax^2 + 15

6 = -a(3^2) + 15

6 = -9a + 15

-9 = -9a

a = 1

y = -x^2 + 15

y=0 when x^2 = 15, so the width is 2√15 at its base

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