Question

Find b and c so that y=-12x^3+bx+c has a vertex (2,-8)

Answer 1

y = -12x² +48x -56

Explanation:

1. Start with the Vertex Form for the equation: y = -12(x-2)² - 8 (notice where I place the x and y coordinates of the vertex).

2. Convert the equation from step 1 to Standard Form by FOILing the (x-2)², distributing the -12, and combining the constant terms:
y = -12(x-2)² - 8
y = -12(x-2)(x-2) - 8
y = -12(x²-4x+4) - 8
y = -12x² +48x -48 -8
y = -12x² +48x -56