What is the axis of symmetry and vertex for the graph # y = x^2 + 4x + 4#?

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Answer 1 · 2016-05-14T14:46:44

#color(blue)("Vertex "->(x,y)->(-2,0)#

#color(blue)("Axis of symmetry "->x=-2#

Consider the standard form #y=ax^2+bx+c#

Write this as #y=a(x^2+b/ax)+c#

Then #x_("vertex") = "axis of symmetry "=(-1/2)xxb/a#

In this case #a=1#

So for #y=x^2+4x+4#

#x_("vertex")=(-1/2)xx4=-2#

So by substitution for #x#

#y_("vertex")=(-2)^2+4(-2)+4" "=" "0#

#color(blue)("Vertex "->(x,y)->(-2,0)#

#color(blue)("Axis of symmetry "->x=-2#