Question

What is the vertex form of `y= 3x^2 - 14x - 10`?

Answer 1

`y=3(x-7/3)^2-79/3`

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

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

`rArry=3(x^2-14/3x-10/3)`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2-14/3x`

`rArry=3(x^2+2(-7/3)xcolor(red)(+49/9)color(red)(-49/9)-10/3)`

`color(white)(rArry)=3(x-7/3)^2+3(-49/9-10/3)`

`color(white)(rArry)=3(x-7/3)^2-79/3larrcolor(red)"in vertex form"`