Question

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

Answer 1

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 = -b/(2a)`
where the quadratic is `y = ax^2 + bx + c`.

Therefore just plug the values in:
`-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