# How do you find the axis of symmetry, and the maximum or minimum value of the function y = x^2 + 4x + 4?

Feb 10, 2016

The axis of symmetry is x = -2
The minimum of the function is 0

#### Explanation:

The formula for the axis of symmetry is given by $x = - \frac{b}{2 a}$
where the quadratic is $y = a {x}^{2} + b x + c$.

Therefore just plug the values in:
$- \frac{4}{2}$ => $x = - 2$ which is the axis of symmetry

Now that we have the x value, we can plug this in to find the y value, which will always be either a max or a min for the axis of symmetry.

We find that y = 0.

If a is positive, there will be a min
If a is negative, there will be a max
(just think back to the parent function $y = {x}^{2}$ ... it opens upwards with a minimum value)

Therefore 0 is the minimum value.
The axis of symmetry is x = -2