Question

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

Answer 1

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

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

Explanation:

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`