Which of the following accurately describes what the graph of y=5x2+50x+125

Let’s analyze the given quadratic function \( y = 5x^2 + 50x + 125 \):

1. Determining the Direction of the Graph: The leading coefficient (the coefficient of \( x^2 \)) is \( 5 \), which is positive. This means the graph opens upward, not downward. Therefore, Statement #1 is false.

2. Finding the Vertex: To find the vertex, we can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 5 \) and \( b = 50 \): \[ x = -\frac{50}{2 \cdot 5} = -\frac{50}{10} = -5. \] The vertex is at \( x = -5 \), which is not to the right of the x-axis (it's at \( x = -5 \)). Hence, Statement #2 is also false.

3. Identifying the Roots: The statement mentions that there is a repeated root at \( x = -5 \). Since it mentions that the graph touches the x-axis once, this is indeed true because a repeated root signifies that the graph just touches the x-axis at that point rather than crossing it. Therefore, Statement #3 is true.

In summary:

• Statement #1: False (Graph opens upward)
• Statement #2: False (Vertex is at \( x = -5 \))
• Statement #3: True (Graph touches the x-axis at \( x = -5 \))

Thus, the accurate description is that only Statement #3 is true.