Question

At which \( x \)-intercept(s) does the graph touch the \( x \)-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) at which the graph touches the \( x \)-axis and turns around is/are \( \square \) . (Type an integer or a decimal. Use a comma to separate answers as needed. Type each answer only once.) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around.

Ask by Moran Bates. in the United States
Mar 19,2025

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Answer

There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around.

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Extra Insights

When a graph touches the \( x \)-axis and turns around, this typically occurs at \( x \)-intercepts with even multiplicity. For instance, if a polynomial has a factor of \((x - a)^2\), the graph will touch the axis at \( x = a \) and bounce back. So, check the function and its factors to find the appropriate intercepts. On the other hand, if you encounter a scenario where there are no such intercepts, it means the polynomial could either trend upwards or downwards without touching the axis. In such cases, polynomials could have all \( x \)-intercepts with odd multiplicities or simply not cross the axis at all.

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