To analyze the given quadratic function \( y = 5x^2 + 50x + 125 \), let's break down the statements based on the given information:
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Finding the vertex: The standard form of a quadratic equation is \( y = ax^2 + bx + c \). Here, \( a = 5 \), \( b = 50 \), and \( c = 125 \).
The vertex \( x \)-coordinate can be found using the formula \( x = -\frac{b}{2a} \): \[ x = -\frac{50}{2 \cdot 5} = -\frac{50}{10} = -5. \] This means that the vertex is at \( x = -5 \).
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Opening direction: Since \( a = 5 > 0 \), the parabola opens upward.
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Roots: Since we have a repeated root at \( x = -5 \), we can conclude that the quadratic does touch the x-axis at this point, meaning the graph has exactly one x-intercept.
Now, we can evaluate the statements:
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Statement #1: "The graph opens downward."
- This is false because the parabola opens upward.
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Statement #2: "The graph has a vertex to the right of the x-axis."
- This is false because the vertex is at \( x = -5 \), which is to the left of the x-axis.
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Statement #3: "The graph touches the x-axis once."
- This is true since there is a repeated root at \( x = -5 \).
In conclusion, the only true statement is Statement #3.
So, the accurate description based on the given information is: Statement #3: True. Statements #1 and #2 are false.