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

Question

2864 views around the world

You can reuse this answer
Creative Commons License

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 $x$

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

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

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

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