Designing a highway Traffic engineers are designing a stretch of highway that will connect...

Designing a highway Traffic engineers are designing a stretch of highway that will connect a horizontal highway with one having a 20% grade (that is, slope ), as illustrated in the figure. The smooth transition is to take place over a horizontal distance of 800 feet, with a parabolic piece of highway used to connect points A and B. If the equation of the parabolic segment is of the form y = ax2 + bx + c, it can be shown that the slope of the tangent line at the point P(x, y) on the parabola is given by m =2ax + b.

(a) Find an equation of the parabola that has a tangent line of slope 0 at A and  at B.

(b) Find the coordinates of B.

EXERCISE