fill in the blanks so that the resulting statement is true.\nif ( r ) is a zero of even multiplicity, then…

Brief Explanations:

When (r) is a zero of even multiplicity for a polynomial function (y = f(x)), the factor ((x - r)) appears an even number of times in the factored form of the polynomial. The graph of the polynomial function (y=f(x)) will touch the (x -)axis at (x = r) and turn around (because the sign of the function does not change on either side of (x=r) for an even - multiplicity zero).

When (r) is a zero of odd multiplicity for a polynomial function (y = f(x)), the factor ((x - r)) appears an odd number of times in the factored form of the polynomial. The graph of the polynomial function (y = f(x)) will cross the (x -)axis at (x=r) (because the sign of the function changes on either side of (x = r) for an odd - multiplicity zero).

Answer:

If (r) is a zero of even multiplicity, then the graph touches the (x) - axis and (\text{turns around}) at (r). If (r) is a zero of odd multiplicity, the graph (\text{crosses}) the (x) - axis at (r).