Graphing Quadratic Functions

Polynomial graphs have basic shapes, depending on the degree, as shown in the table.

Polynomial Function	Degree	Graph
Constant	0	Horizontal line
Linear	1	Line with slope
Quadratic	2	Parabola
Cubic	3	S-shaped curve
Quartic	4	U-shaped curve with some potential "ups" and "downs" in the middle of the graph.

Since the graph of a polynomial function is a continuously smooth curve, by plotting the intercepts, we can draw a rough sketch of the graph. For our purposes in this unit, we will only look at the graphs of Quadratic Functions.

parabola that opens at the top on a graph denoting the axis of symmetry, x-intercepts (solutions), y-intercept, and the vertex

graph with a parabola that opens down denoting the maximum at the vertex and the axis of symmetry

parabola on a graph that opens up denoting the axis of symmetry and the minimum at the vertex

Now it is time for you to practice a little. Please complete the following Graphing Quadratic Functions Self-Assessment.

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