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`

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

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

Taking square root on both sides, we get

`x-4=√(4)`

`\:x-4=√(4) \ and \ x-4=-√(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.