College Math CLEP Prep Practice Exam

What type of graph is generated when a polynomial with even degree has its roots in the x-axis?

1. Parabola

2. Ellipse

3. Hyperbola

4. Line

The correct answer is: Parabola

A polynomial with even degree has a graph that will display symmetry along the y-axis as the degree increases or decreases. When the roots of a polynomial equation are placed on the x-axis, the graph transforms into a parabola. Thus, the correct answer is A. The graph will not be an ellipse, as an ellipse is the graph of a circle that is rotated around its center which is given by a different kind of equation. Also, there cannot be a hyperbola, as a hyperbola is a curve on a plane, that consists of two separate parts and each of which tends toward infinity. Lastly, a line as a graph is not possible since the degree of a line is only one and the roots on a line cannot be placed in the same location.