Question

How do I use the vertex formula to determine the vertex of the graph of the function and write it in standard form for `2x^2+6x-1`?

Answer 1

`y = 2x^2+6x-1` is already in standard form

`color(white)("XXXXX")`General standard form for a parabola is `y=ax^2+bx+c`

Vertex form for a parabola is `y =m(x-a)+b`
`color(white)("XXXXX")`Note: the `a and b` are not the same as in the standard form but they are constants.

`y=2x^2+6x+1`
`color(white)("XXXXX")`extract `m`
`y= 2(x^2+3x) + 1`
`color(white)("XXXXX")`complete the square
`y=2(x^2+3x+(3/2)^2) +1 - 9/2`

`y = 2(x+3/2)^2 -7/2`

`y = 2(x-(-3))^2+(-7/2)`
`color(white)("XXXXX")`which is in vertex form with a vertex at `(-3,-7/2)`