Question

What is the vertex of `y= 2(x - 4)^2 - x^2+3`?

Answer 1

Vertex (8, -29)

Explanation:

Develop `y = 2(x - 4)^2 - x^2 + 3 = 2(x^2 - 8x + 16) - x^2 + 3 =`
`= 2x^2 - 16x + 32 - x^2 + 3 = x^2 - 16x + 35.`

x-coordinate of vertex:
`x = -b/(2a) = 16/2 = 8`
y-coordinate of vertex:
`y(8) = 64 - 16(8) + 35 = -64 + 35 = -29`

Vertex (8, -29)