Question

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

Answer 1

(4,24)

Explanation:

Simplify first
`y= -3x^2-4x+2(x-2)^2`
`y= -3x^2 -4x + 2(x^2+4x+4)`
`y= -3x^2 -4x + 2x^2 +8x+8`
`y= -x^2 +8x+8`

Now to solve for the vertex algebraically , we use the formula
Vertex= `( -b/(2a) , f(-b/(2a) ) )`
`-b/(2a) = 4`
`f(4)= 24`

Vertex = (4,24)