Problem: If in applying the quadratic formula to a quadratic equation , it happens that , then the graph of will certainly:
Answer Choices:
A. have a maximum
B. have a minimum
C. be tangent to the -axis
D. be tangent to the -axis
E. lie in one quadrant only
Solution:
The condition implies equal real roots of for real coefficients, i.e., the curve touches the -axis at exactly one point and, therefore, the graph is tangent to the -axis.