Question

What is the vertex of `y=x^2 +5(x-3)^2`?

Answer 1

The vertex is `(5/sqrt(2), -30)`

Explanation:

Expand and simplify the expression first
`y = x^2 +5(x^2 -6x + 9)`
`y = 6x^2 -30x +45`
`y= 3(2x^2 -10x +15)`
The use completing the square to get vertex form
`y = 3((sqrt(2)x -5)^2 -25 + 15)`
`y = 3(sqrt(2)x - 5)^2 -30`
The vertex is `(5/sqrt(2), -30)`