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

##### 1 Answer

May 18, 2018

#### 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]}