Question

The x-coordinate of the vertex of the equation y = 2x2 − 4x + 12 The x-coordinate of the vertex of the equation y = 4x2 + 8x + 3

Answer 1

So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is $x=\frac{-b}{2a}$, with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:

y = 2x^2 − 4x + 12: $x=\frac{4}{2*2}=\frac{4}{4}=1$

y = 4x^2 + 8x + 3: $x=\frac{-8}{2*4}=\frac{-8}{8}=-1$

In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.