The parabola y=ax^2+bx+c has vertex (p,p) and y-intercept (0,-p), where p≠ 0. What is b?

Question

I just want to know how to solve this.

Answer 1

The governing equation is y = -(2/p)x² + 4x -p so therefore, b = 4.

Why? The parabolic form of the equation which is y =a(x-h)² + k transforms into

y = a(x-p)² + p because of the vertex being (h,k) = (p,p) To find a, we use the other condition

the intercept is (0,-p). When you substitute, you get a = -(2/p) So the parabolic equation is

y = -(2/p)(x-p)² + p and when you multiply this out, you get y = -(2/p)x² + 4x -p