Question

How do you find the vertex and axis of symmetry for `y = 1/2x^2 + 8x - 9`?

Answer 1

Convert the given equation into vertex form to get the vertex at `(-8,-41)`

Explanation:

Vertex form of a quadratic:
`color(white)("XXXX")` `y =m(x-a)^2+b`
`color(white)("XXXX")` `color(white)("XXXX")`with vertex at `(a,b)`

Given `y= 1/2x^2+8x-9`

Extract `m`
`color(white)("XXXX")` `y = (1/2)(x^2+16x) -9`

Complete the square
`color(white)("XXXX")` `y = (1/2)(x^2+16x+64) -9 - (1/2)(64)`

Simplify into vertex form:
`color(white)("XXXX")` `y = (1/2)(x+8)^2 -41`
`color(white)("XXXX")`or
`color(white)("XXXX")` `y = (1/2)(x-(-8)) + (-41)`