Question

Please help!!! 15 points problem below

Answer 1

We are given height function of the bridge

h(x) =-0.5(x-4)^2 +2.

Where height is the height of the bridge in feet and x is the distance between two bases.

We have height =0 on the base of the bridge. In order to find the both bases, we need to plug h(x) as 0 and solve for x.

-0.5(x-4)^2 +2 = 0

$\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}$

$-0.5\left(x-4\right)^2+2-2=0-2$

$-0.5\left(x-4\right)^2=-2$

$\mathrm{Multiply\:both\:sides\:by\:}10$

$-0.5\left(x-4\right)^2\cdot \:10=-2\cdot \:10$

$-5\left(x-4\right)^2=-20$

$\mathrm{Divide\:both\:sides\:by\:}-5$

$\frac{-5\left(x-4\right)^2}{-5}=\frac{-20}{-5}$

$\left(x-4\right)^2=4$

Taking square root on both sides, we get

$x-4=\sqrt{4}$

$\:x-4=\sqrt{4} \ and \ x-4=-\sqrt{4}$

$x-4=2 \\x-4=-2$

$x=6,\:x=2$

We got horizontal distances 2 feet and 6 feet.

Therefore, correct option is D.