Questions: Fill in the blanks so that the resulting statement is true. If r is a zero of even multiplicity, then the graph touches the x-axis and flattens out at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis at r. steepens crosses flattens out turns around

Solution Steps

To fill in the blanks, we need to understand the behavior of polynomial graphs at their zeros based on the multiplicity of the zeros. For a zero of even multiplicity, the graph touches the x-axis and turns around at that point. For a zero of odd multiplicity, the graph crosses the x-axis at that point.

For a zero \( r \) of even multiplicity, the graph of the polynomial touches the \( x \)-axis at \( r \) and turns around. This means that the graph does not cross the \( x \)-axis but instead bounces off it.

For a zero \( r \) of odd multiplicity, the graph of the polynomial crosses the \( x \)-axis at \( r \). This indicates that the graph changes direction as it passes through the \( x \)-axis.

Final Answer