Question
Which of the following accurately describes what the graph of y=5x2+50x+125
looks like, with the repeated root of x=−5
?(1 point)
Responses
The graph tastes like tacos
The graph tastes like tacos
The graph opens downward
The graph opens downward
The graph has a vertex to the right of the y-axis
The graph has a vertex to the right of the y-axis
The graph touches the x-axis once
The graph touches the x-axis once
looks like, with the repeated root of x=−5
?(1 point)
Responses
The graph tastes like tacos
The graph tastes like tacos
The graph opens downward
The graph opens downward
The graph has a vertex to the right of the y-axis
The graph has a vertex to the right of the y-axis
The graph touches the x-axis once
The graph touches the x-axis once
Answers
GPT-4o mini
To analyze the graph of the quadratic function \( y = 5x^2 + 50x + 125 \), we can look at its properties based on its equation.
1. **The graph opens downward**: This is incorrect. Since the coefficient of \( x^2 \) (which is 5) is positive, the graph opens upward.
2. **The graph has a vertex to the right of the y-axis**: This is incorrect. To determine the vertex's location, we can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 5 \) and \( b = 50 \):
\[
x = -\frac{50}{2 \cdot 5} = -\frac{50}{10} = -5
\]
Since -5 is to the left of the y-axis, this statement is false.
3. **The graph touches the x-axis once**: This is correct. A graph that touches the x-axis at one point (the repeated root \( x = -5 \)) indicates that there is a double root, signifying that the graph only meets the x-axis at that point and does not cross it.
Thus, the correct response is: **The graph touches the x-axis once**.
1. **The graph opens downward**: This is incorrect. Since the coefficient of \( x^2 \) (which is 5) is positive, the graph opens upward.
2. **The graph has a vertex to the right of the y-axis**: This is incorrect. To determine the vertex's location, we can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 5 \) and \( b = 50 \):
\[
x = -\frac{50}{2 \cdot 5} = -\frac{50}{10} = -5
\]
Since -5 is to the left of the y-axis, this statement is false.
3. **The graph touches the x-axis once**: This is correct. A graph that touches the x-axis at one point (the repeated root \( x = -5 \)) indicates that there is a double root, signifying that the graph only meets the x-axis at that point and does not cross it.
Thus, the correct response is: **The graph touches the x-axis once**.