Question

How do you write the vertex form equation of the parabola `3x^2+30x-y+71=0`?

Answer 1

`y=3(x+5)^2-4`

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 "color(blue)"completing the square"`

`"express as "y=3x^2+30x+71`

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

`rArry=3(x^2+10x+71/3)`

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

`rArry=3(x^2+2(5)xcolor(red)(+25)color(red)(-25)+71/3)`

`color(white)(rArry)=3(x+5)^2+3(-75/3+71/3)`

`color(white)(rArry)=3(x+5)^2-4larrcolor(red)"in vertex form"`