Question

What is the vertex form of `y= (3x-8)(-6x-2)+2x^2+3x`?

Answer 1

Vertex `(45/32, 3049/64)`

Explanation:

`y=(3x-8)(-6x-2)+2x^2+3x`

`y=-18x^2-6x+48x+16+2x^2+3x`

`y=-16x^2+45x+16`

The vertex is found by `x=-b/(2a)`

By looking at the general formula of a quadratic function,
`y=ax^2+bx+c` , we can see that `b=45` and `a=-16`

`x=-b/(2a) = -45/(2times-16) = 45/32`

Sub `x=45/32` into `y=-16x^2+45x+16`

`y=-16(45/32)^2+45(45/32)+16`
`y= 3049/64`

Vertex `(45/32, 3049/64)`

You can from the graph below that the vertex is quite high up.

graph{(3x-8)(-6x-2)+2x^2+3x [-10, 10, -5, 5]}