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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?

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Solution Preview


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.