Question

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

Answer 1

vertex(-2 ,-2) axis of symmetry x = -2

Explanation:

Begin by `color(blue)" completing the square "`

This is achieved by adding`" (1/2 coefficient of x-term)"^2"`

here the coefficient of the x-term = 4

so we require `x^2+4x+(2)^2 +2`

`y=x^2+4x+4+2-4 = (x+2)^2-2`

Require to subtract 4 since it was added on.

Now the equation in vertex form is `y=a(x-h)^2+k`
where (h ,k) is the vertex.

`rArr " vertex "=(-2,-2)"`

The axis of symmetry passes through the x-coordinate of the vertex.

`rArr " equation is x = -2"`
graph{x^2+4x+2 [-10, 10, -5, 5]}