Question

What is the axis of symmetry and vertex for the graph `y=x^2+8x+12`?

Answer 1

`x=-4" and vertex "=(-4,-4)`

Explanation:

`"given a parabola in standard form "color(white)(x);ax^2+bx+c`

`"then the x-coordinate of the vertex which is also the "`
`"equation of the axis of symmetry is"`

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

`y=x^2+8x+12" is in standard form"`

`"with "a=1,b=8" and "c=12`

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

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

`y_("vertex")=(-4)^2+8(-4)+12=-4`

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

`"axis of symmetry is "x=-4`
graph{(y-x^2-8x-12)(y-1000x-4000)=0 [-10, 10, -5, 5]}