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True and False about Characteristics of a Parabola

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These questions are about the quadratic function which takes the form:

y=ax^2+bx+c

Where a is non-zero.

Choose the false statements.

A. If c=0, then the graph of y will go through the origin

B. If B=0, then the graph of y will not be a parabola.

C. The graph of y will have a minimum value if a is positive.

D. The graph of y will always cross the x-axis.

E. The graph of y will always cross the y-axis.

F. The graph of y is symmetric about a line through its vertex parallel to the y-axis.

G. If the graph of y just touches the x-axis the equation y=0 has just one solution.

H. The function y takes its maximum or minimum value when the gradient takes the value zero.

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Solution Summary

True and false questions about the characteristics of the parabola are answered with reasons.

Solution Preview

The two false answers are B and D.
The reason for option B is that if b=0 the graph of y is still a ...

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