Question

What is the vertex of `y= 2(x-5)^2-5x^2-x-1`?

Answer 1

The vertex is `(-7/2, 343/4)`

Explanation:

First expand the equation to get rid of the brackets and into standard form. The expression can then be rearranged into vertex to identify the vertex.

`y = 2(x^2 -10x +25) - 5x^2 - x -1`
`y= -3x^2 -21x +49`
`y = -3(x^2 +7x) +49`

`y = -3(x+7/2)^2 +147/4 + 49`
`y = -3(x+7/2)^2 +343/4`

The vertex is `(-7/2, 343/4)`