Learning Resources

Shapes of Polynomial Functions

• For equations 1 and 2, the x-intercepts occur at the roots of the quadratic. Notice that the second quadratic had 2 equal real roots, meaning the graph really only hits the x-axis once. This, of course, would have to occur at the vertex. 
• The roots of the third equation, however, are imaginary. Thus the graph will not hit the x-axis, indicating that there are no x-intercepts.