During a pumpkin launching contest, two pumpkins are launched at the same time. the path of pumpkin a is modeled by the equation h(x) = –0.01x2 + 0.32x + 4. the path of pumpkin b is modeled by the equation h(x) = –0.01x2 + 0.18x + 5. if x represents the distance the pumpkin traveled and h(x) represents height, what does the intersection point of the equations represent?

D.) The distance at which the height of the pumpkins are the same.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4