Question Given the equation y=−10x2+20x+80 with solutions of x=−2 and x=4 , which of the following identifies the general shape of its associated graph?(1 point) Responses The graph touches the x-axis exactly one time. The graph touches the x -axis exactly one time. The vertex is to the left of the y-axis. The vertex is to the left of the y -axis. The graph opens upward. The graph opens upward. The graph opens downward.

Question

Question Given the equation y=−10x2+20x+80 with solutions of x=−2 and x=4 , which of the following identifies the general shape of its associated graph?(1 point) Responses The graph touches the x-axis exactly one time. The graph touches the x -axis exactly one time. The vertex is to the left of the y-axis. The vertex is to the left of the y -axis. The graph opens upward. The graph opens upward. The graph opens downward.

Answer 1

The correct response is:

The graph touches the x-axis exactly one time.
The vertex is to the right of the y-axis.
The graph opens downward.

This is because the equation y = -10x^2 + 20x + 80 is in the form of a quadratic function, where the coefficient of x^2 is negative (-10). This indicates that the graph opens downward. The fact that the solutions are x = -2 and x = 4 means that the graph intersects the x-axis at those points. The vertex of the parabola, which represents the highest or lowest point of the graph, is to the right of the y-axis.