Given the equation y=3x2−24x+48 with solutions of x=4 and x=4 , which of the following identifies the general shape of its associated graph?(1 point)

To determine the general shape of the graph of the quadratic equation \( y = 3x^2 - 24x + 48 \), we need to analyze its properties.

1. **Coefficient of \( x^2 \)**: The equation is of the form \( y = ax^2 + bx + c \), where \( a = 3 \), \( b = -24 \), and \( c = 48 \). Since \( a > 0 \), the graph opens **upward**.

2. **Vertex Location**: The x-coordinate of the vertex of a parabola given by \( y = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \).
- Here, \( -\frac{b}{2a} = -\frac{-24}{2 \cdot 3} = \frac{24}{6} = 4 \).
- Since the vertex's x-coordinate (which is 4) is on the right side of the y-axis, we can say that the vertex is to the **right** of the y-axis.

3. **Solutions**: The given solutions \( x = 4 \) are repeated (indicating that the vertex is located at that point in terms of x, which means the graph touches the x-axis at \( (4, 0) \) and does not cross it).

Therefore, we can summarize the results:
- The graph opens **upward**.
- The vertex is located on the x-axis and not to the left of the y-axis.
- The graph does cross the x-axis at \( (4, 0) \), meaning that it does not lie entirely above the x-axis.

From the options provided, the appropriate response is **"The graph opens upward."**