Question

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

Answer 1

The vertex form for a quadratic looks like: `y=a(x-h)^2+k`. Once you know that the vertex is at (-4,2), you can find out lots of other information!

Explanation:

The axis of symmetry must go through the vertex, so it is the line `x = -4`.

Since the leading coefficient, or multiplier on `x` is 1, and 1 is positive, the parabola will open upward. This means that the graph will have a minimum rather than a maximum. The minimum is the y-value from the vertex: 2.

Here is the graph: