Question

What is the vertex form of `y= -9x^2+11x-1`?

Answer 1

`y=-9(x-11/18)^2+85/36`

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 constant.

`"using the method of "color(blue)"completing the square"`

add `(1/2"coefficient of x-term")^2" to " x^2-11/9x`

Since we are adding a value that is not there we must also subtract it.

`"that is add/subtract" ((-11/9)/2)^2=121/324`

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

`y=-9(x^2-11/9x)-1larrcolor(red)" coefficient now 1"`

`rArry=-9(x^2-11/9xcolor(red)(+121/324 -121/324))-1`

`color(white)(rArry)=-9(x-11/18)^2+121/36-1`

`color(white)(rArry)=-9(x-11/18)^2+85/36larrcolor(red)" in vertex form"`