What is the approximate value of the \( y \)-intercept? The x-axis spans from below negative 5 to 5, and the y-axis spans from below negative 20 to above zero. The x-axis has a scale of 5 in increments of 1 and the y-axis has a scale of 10 in increments of 2. The red curve represents a polynomial function with four turning points. It begins from the bottom-middle of the third quadrant, reaches a local maximum at (negative 3, 0), then drops steeply to a local minimum near (negative 1.5, negative 21). It rises again to another local maximum near (0.5, 0.8), falls to a local minimum around (1, 0), and then steeply extends upward out of view.

Which function is represented by the graph shown? “The x-axis spans from negative 10 to 10, and the y-axis spans from negative 5 to just above 15. Both axes have a scale of 5 in increments of 1. The purple V-shaped function consists of two linear segments meeting at a sharp vertex at the coordinate (negative 2, 1). The left segment is in the second quadrant with a negative slope, passing through the point (negative 5, 13). The right segment spans the second and the first quadrants, with a positive slope, passing through the y-axis at (0, 9). The function is symmetric around the vertical line x= negative two and extends out of view in both directions. “

If one root of a polynomial is \( 3 – 2i \), what is the other root assuming the polynomial has real coefficients?

A city park is designing a walking path that must meet two elevation-related safety guidelines:y = x^2 – 4 The maximum allowed elevation (in feet) along the path is modeled by the equation , where is the horizontal distance (in meters) from the park entrance. For water drainage purposes, the path must stay above the line . The constraints are represented in the graph: What does the solution to this system represent in context? “The x-axis and the y-axis span from below negative 5 to above 5, with a scale of 5 in increments of 1. A solid blue parabola opens upward with its vertex at (0, negative 4), enclosing a white region inside. The parabola passes through the coordinates (negative 2, 0) and (2, 0), extending upward. The area around the parabola is shaded in light blue. A dashed orange diagonal line with a positive slope passes through the points (0, -1) and (-2, -5). The line intersects the parabola at (negative 1, negative 3) and (3, 5), while the area above the line is shaded orange. This orange-shaded area overlaps the blue area as well as most of the white region inside the parabola. The overlap spans the second quadrant, most of the third quadrant, and a small portion of the first quadrant. The overlap on the blue area appears brown, while over the white parabolic region, it appears orange. The lower-right portion of the parabolic region remains white without any overlap. “

Which transformation occurs when \( g(x) = f(-x) \)?

Multiply the following rational expressions: \[\frac{2x}{x^2 – x – 6} \times \frac{x – 3}{x}\]

Simplify the product: \[\frac{x^2 – 4x + 4}{x^2 – 9} \cdot \frac{x – 3}{x – 2}\]

What is the end behavior of the polynomial function? The x-axis spans from negative 4 to 4, and the y-axis spans from below negative 10 to above 10. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 10 in increments of 2. The orange polynomial function has an inflection point around the origin (0,0), with a local maximum at approximately (negative 0.5, 1) and a local minimum near (1.25, negative 2). The function decreases from negative infinity, rises to the local maximum, falls to the local minimum, and then increases towards positive infinity, extending out of view at both ends. 

Which binomials are factors of the polynomial shown?  The x-axis spans from negative 4 to beyond 2, and the y-axis spans from below negative 5 to 10. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 5 in increments of 1. The green polynomial function has a local minimum at (negative 2, 0) and a local maximum at (0, 8). The function decreases from the top left of the second quadrant, reaching its minimum, then increases to its maximum on the y-axis before decreasing again, passing through the point (1, 0) and continuing into the fourth quadrant. The curve continues to extend out of view in both directions.

What are the roots of the parabola shown? The x-axis spans from below negative 5 to above 5, and the y-axis spans from below negative10 to 20. The x-axis has a scale of 5 in increments of 1 and the y-axis has a scale of 10 in increments of 2. The green parabola opens upward, with its vertex at approximately (0, negative 9). The curve is symmetric around the y-axis. It crosses the x-axis at (negative 3, 0) and (3, 0), extending out of view at both ends.