Question

Highway engineers design a parabolic curve for an entrance ramp from a straight street to an interstate highway. The vertex of the curve passes through (0, 0) and the parabola passes through (1000, + 800). Find an equation for the parabola.

Answer 1

two situation:
1.the curve opens up.

so the equation is \[ay=x ^{2}\]
we substituted (1000,800) into the equation and find that a=0.04
so it is\[0.04y=x ^{2}\]
2. the curve opens right

so the equation is \[y ^{2}=ax\]
we substituted (1000,800) into the equation and find that a=0.03
so it is\[y ^{2}=0.03x\]