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=(-b)/(2a)`, with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:

y = 2x^2 − 4x + 12:
`x=(4)/(2*2)=(4)/(4)=1`

y = 4x^2 + 8x + 3:
`x=(-8)/(2*4)=(-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.