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 graph opens downward
the vertex is to the left of the y-axis
the graph touches the x-axis exactly one time
the graph opens upward
The correct answer is: the graph opens downward.
To determine the general shape of the graph associated with the given equation, we can analyze the coefficient of the x^2 term, which is -10.
If the coefficient of the x^2 term is negative, as it is in this case (-10), the graph opens downward. This means that the correct answer is:
- the graph opens downward.
To determine the general shape of the graph associated with the equation y = -10x^2 + 20x + 80, we need to analyze the coefficient of the x^2 term, which is -10.
If the coefficient of the x^2 term is positive, like in this case, the graph opens upward. On the other hand, if the coefficient is negative, the graph opens downward.
Therefore, the correct answer is: the graph opens upward.