Given the equation y=−x2+2x+48 with solutions of x=−6 and x=8 , which of the following identifies the general shape of its associated graph?(1 point) Responses The graph crosses the x-axis at x=−6 and x=8 . The graph crosses the x -axis at x equals negative 6 and x equals 8 . The vertex is to the left of the y-axis. The vertex is to the left of the y -axis. The graph has the shape of a straight line. The graph has the shape of a straight line. The graph opens upward.

Question

Given the equation y=−x2+2x+48 with solutions of x=−6 and x=8 , which of the following identifies the general shape of its associated graph?(1 point) Responses The graph crosses the x-axis at x=−6 and x=8 . The graph crosses the x -axis at x equals negative 6 and x equals 8 . The vertex is to the left of the y-axis. The vertex is to the left of the y -axis. The graph has the shape of a straight line. The graph has the shape of a straight line. The graph opens upward.

Answer 1

To determine the general shape of the graph of the equation y = -x^2 + 2x + 48, we can analyze the coefficients of the equation.

In this equation, the coefficient of x^2 is -1, which indicates that the graph is a downward-facing parabola. A negative coefficient in front of x^2 indicates a concave shape downwards.

Since the coefficient of x^2 is negative, we can conclude that the graph opens downward (not upward) and the vertex is at the highest point of the parabola.

Therefore, the correct response is: The graph opens upward.