Question

Write an equation in intercept form of the parabola that passes through the point (3,40) and has x-intercepts −5 and 4.

Answer 1

The equation of this parabola will have the form f(x) = a(x+5)(x-4), which works out to f(x) = a(x^2 + x - 20).  Since the parabola passes thru (3,40),

40 = a(3^2 + 3 - 20), or 40 = a(-8), so a = -5.

Thus, the equation of this parabola is     y = -5(x^2 + x - 20).