Question

How do you write the quadratic function `y=3x^2-9x+18` in vertex form?

Answer 1

`y=3(x-3/2)^2+45/4`

Explanation:

`"the equation of a quadratic function 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.

`"rearrange " y=3x^2-9x+18" into this form"`

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

`" coefficient of " x^2" must be unity"`

`rArr3(x^2-3x)+18`

add `(1/2"coefficient of x-term")^2 " to " x^2-3x`

`"we must also subtract this value, since it is not"`
`"there to start with"`

`"that is add/subtract " (-3/2)^2=9/4`

`rArr3(x^2-3xcolor(red)(+9/4)color(red)(-9/4))+18`

`=3(x-3/2)^2-27/4+18`

`rArry=3(x-3/2)^2+45/4larrcolor(red)" in vertex form"`