Question

What is the the vertex of `y =-2x^2 + 12x + 9`?

Answer 1

`"vertex "=(3,27)`

Explanation:

`"given a quadratic in "color(blue)"standard form ";ax^2+bx+c`

`"then the x-coordinate of the vertex is "`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)`

`-2x^2+12x+9" is in standard form"`

`"with "a=-2,b=12" and "c=9`

`x_("vertex")=-12/(-4)=3`

`"substitute this value into the equation for y"`

`y_("vertex")=-2(3)^2+12(3)+9=27`

`color(magenta)"vertex "=(3,27)`