Question

How do you write `g(x)=2x^2+8x+13` in vertex form?

Answer 1

`g(x)=2(x+2)^2+5`

Explanation:

`"given the parabola in standard form "ax^2+bx+c`

`"the x-coordinate of the vertex is"`

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

`2x^2+8x+13" is in standard form"`

`"with "a=2,b=8,c=13`

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

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

`rArry_(color(red)"vertex")=2(-2)^2+8(-2)+13=5`

`rArrcolor(magenta)"vertex "=(-2,5)`

`"the equation of the parabola in "color(blue)"vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a constant"`

`"here "a=2" and "(h,k)=(-2,5)`

`rArrg(x)=2(x+2)^2+5larrcolor(red)" in vertex form"`