# Graphing Functions: Completing the Square, Quadratic Functions, Axis of Symmetry, and Intercepts

1. Using completing the square to describe the graph of the following function. Support your answer graphically.

f(x) = -2x^2 + 4x + 1

2. Graph the function: g(x) = (x-2)^3

3. Determine the quadratic function f whose vertex is (3, -2) and passes through (2, 1)

4. Graph the line containing the point P and having slope m: P = (2, -7); m = 0

5. Graph the function and state the vertex, the axis of symmetry, the intercepts, if any: f(x) = x^2-6x+5

What is the vertex?

What is the axis of symmetry?

What are the intercepts, if any?

https://brainmass.com/math/graphs-and-functions/completing-square-quadratic-functions-axis-symmetry-543240

#### Solution Preview

1.

This parabola has a vertex at

We see that as the function approaches , so the vertex point is a maxima (the parabola opens down).

The parabola intersects the x-axis when

Which gives:

It intersects the y-axis when x=0 and this gives:

To summarize:

The parabola has a vertex which is a maxima at so its symmetry axis is x=1

It intersects the x-axis at and

It intersects the y-axis at ...

#### Solution Summary

The solution assists with completing the square, quadratic functions, axis of symmetry and intercepts. The axis of symmetry and intercepts are analyzed.