Question

What is the vertex form of `y=-x^2+5x-5`?

Answer 1

`y=-(x-5/2)^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"`

`"to obtain this form use "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1"`

`"factor out "-1`

`y=-(x^2-5x+5)`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2-5x`

`y=-(x^2+2(-5/2)x color(red)(+25/4)color(red)(-25/4)+5)`

`color(white)(y)=-(x-5/2)^2-(-25/4+5)`

`rArry=-(x-5/2)^2+5/4larrcolor(red)"in vertex form"`