Question

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

Answer 1

`f(x)=-3(x-1/2)^2-5/4`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"given the parabola in "color(blue)"standard form"`

`f(x)=ax^2+bx+c color(white)(x);a!=0`

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

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

`f(x)=-3x^2+3x-2" is in standard form"`

`"with "a=-3,b=3" and "c=-2`

`rArrx_(color(red)"vertex")=-3/(-6)=1/2`

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

`y_(color(red)"vertex")=-3(1/2)^2+3(1/2)-2=-5/4`

`rArrf(x)=-3(x-1/2)^2-5/4larrcolor(red)"in vertex form"`