Properties of Quadratic Equations

Question

Given that the standard form of a quadratic equation follows the form y = ax²+bx+c,

Show why the vertex always falls on the line y = bx/2 + c (Hint: Consider the coordinate pair of the vertex)

Then, give a quadratic equation that models the vertex given that b = t and t varies. (Hint: this equation is intersected at 2 points by the line y = bx/2 + c when a,b ≠ 0)

Answer 1

The axis of symmetry is x = -b / 2a

The y-coordinate is

y = a(-b/2a)² + b(-b/2a) + c