Finding Negative Values of f(x) in a Quadratic Function with Given X-Axis Intersections

The graph of the function below intersects the $x$-axis at points A and B.

The vertex of the parabola is marked at point C.

Find all values of $x$
where$f\left(x\right) < 0$.

To solve this problem, let's analyze the graph of this quadratic function:

• The graph intersects the $x$-axis at points A and B, indicating $f(x) = 0$ at these points.
• The function exhibits a parabolic shape with a vertex located at point C, below the $x$-axis, suggesting that the parabola opens upwards.

For a typical upward opening parabola that intersects the $x$-axis at A and B, the function $f(x)$ is below the $x$-axis (i.e., $f(x) < 0$) outside the interval between A and B.

Therefore, the solution set for which $f(x) < 0$ is $x < A$ or $x > B$. This represents where the parabola lies beneath the $x$-axis.

This corresponds to choice 2: $x > B$ or $x < A$.