Given the equation y = 3x^2 - 24x + 48 with solutions of x = 4 and x = 4, which of the following identifies the general shape of its associated graph?
the graph opens downward
the graph opens upward
the vertex is to the left of the y-axis
the entire graph lies above the x-axis
The correct answer is:
the graph opens upward
To determine the general shape of the graph associated with the equation y = 3x^2 - 24x + 48, we need to look at the coefficient of x^2. In this case, the coefficient is positive (3), which means the parabola opens upward.
Therefore, the correct choice is: the graph opens upward.
To determine the general shape of the graph of the equation y = 3x^2 - 24x + 48, we need to examine the coefficient of the x^2 term, which is 3.
If the coefficient of the x^2 term is positive, like in this case, the graph opens upward. This means that the parabola formed by the equation will have a U-shape, and the vertex of the parabola will be the lowest point on the graph.
Therefore, the correct answer is: the graph opens upward.