Question

What is the vertex form of `y=3x^2 +10x - 8`?

Answer 1

`y=3(x+5/3)^2-49/3`

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+10/3x)-8`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2+10/3x`

`rArry=3(x^2+2(5/3)xcolor(red)(+25/9)color(red)(-25/9))-8`

`color(white)(rArry)=3(x+5/3)^2-75/9-8`

`rArry=3(x+5/3)^2-49/3larrcolor(red)"in vertex form"`