Question

What is the vertex form of #y=3x^2 -7x+5?

Answer 1

`y=3(x-7/6)^2+11/12`

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 "color(blue)"complete the square"`

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

`"factor out 3"`

`y=3(x^2-7/3x+5/3)`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2-7/3x`

`y=3(x^2+2(-7/6)x color(red)(+49/36)color(red)(-49/36)+5/3)`

`color(white)(y)=3(x-7/6)^2+3(-49/36+5/3)`

`color(white)(y)=3(x-7/6)^2+11/12larrcolor(red)"in vertex form"`