Question

is it always true that the y-values of a quadratic function have opposite signs on either side of a zero of the function? Explain why or give a counterexample.

Answer 1

Answer:

It is true both sides have opposite signs

Answer 2

By finding a counterexample, y = x^2, we will see that the statement is false.

Is the statement true?

Let's find a counterexample of the given statement.

Suppose that we have the quadratic equation:

y = x^2

The statement says that the y-values have opposite signs on either side of a zero of the function, for the above one the zero is at x = 0.

Now, notice that:

if x = -1

y = (-1)^2 = 1

if x = 1

y = (1)^2 = 1

Then we can see that in both sides of the zero, the y-value has the same sign, then the statement is false.

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