Learning Resources

Shapes of Polynomial Functions

Step B

• If the equation has two different real roots and two equal real roots, the graph will cross the x-axis at each value of the different roots and will just touch the x-axis at the value of the equal roots. The graph will begin in the second quadrant and finish in the first.
• There are three possible shapes for the case where there are two unequal real roots and two complex roots. If a > 0, the graph begins in the second quadrant and finishes in the first. The graph crosses the x-axis twice, at the value of each of the real roots. If a < 0, the graphs are inverted, starting in the third quadrant and ending in the fourth.