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

May 14, 2016

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

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

#### Explanation:

Consider the standard form $y = a {x}^{2} + b x + c$

Write this as $y = a \left({x}^{2} + \frac{b}{a} x\right) + c$

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

In this case $a = 1$

So for $y = {x}^{2} + 4 x + 4$

${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times 4 = - 2$

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