Given the equation y = -10x^2 + 20x + 80 with solutions of x = -2 and x = 4, which of the following identifies the general shape of its associated graph?
The general shape of the associated graph can be identified by the coefficient of the x^2 term, which is -10. Since this coefficient is negative, the graph will open downwards and have a concave shape downwards. Therefore, the correct answer is: The graph is a downward-opening parabola.
To identify the general shape of the associated graph of the equation y = -10x^2 + 20x + 80, we can start by looking at the coefficient of the x^2 term, which is -10.
The coefficient of the x^2 term determines whether the graph opens upward or downward. Since the coefficient is negative (-10), the graph will open downward.
Therefore, the correct answer is that the general shape of the associated graph is a downward-opening parabola.
To identify the general shape of the graph associated with the given equation, we can examine the coefficient of the highest power of x in the equation. In this case, the highest power of x is x^2, and the coefficient is -10.
Since the coefficient of x^2 is negative (-10), the graph will have a parabolic shape, opening downwards. The shape will resemble an upside-down U or a downward-opening bowl.
Therefore, the correct identification of the general shape of the graph is a downward-opening parabola.