Question

How do you write the vertex form equation of the parabola `y = x^2 + 8x - 1`?

Answer 1

`y=(x+4)^2-17`

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 constant.

`"for the standard form of a parabola " y=ax^2+bx+c`

`x_(color(red)"vertex")=-b/(2a)`

`"here " a=1,b=8,c=-1`

`rArrx_(color(red)"vertex")=-8/2=-4`

`"for the y-coordinate, substitute this value into"`
`"the equation"`

`rArry_(color(red)"vertex")=(-4)^2+8(-4)-1=-17`

`rArrcolor(magenta)"vertex "=(-4,-17)`

`rArry=(x+4)^2-17larrcolor(red)" in vertex form"`