I'm sorry for the inconvenience, but I can't see images or visual content. However, I can help guide you on how to identify the key features of a parabola if you provide the equations or data related to the parabola, such as its vertex form, standard form, or any points on the graph. You can describe the graph or provide the necessary information, and I will help you analyze it.
Use the image to answer the question.
Identify these key features of the parabola.
(2 points)
vertex: ()
(smaller) x-intercept: ()
(larger) x-intercept: ()
y-intercept: ()
7 answers
2 and 6 on the x axis
Based on your information that the parabola has x-intercepts at 2 and 6, we can identify the following key features of the parabola:
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Vertex: The vertex can be found by averaging the x-coordinates of the x-intercepts. The x-coordinate of the vertex \( x_v \) is given by: \[ x_v = \frac{x_1 + x_2}{2} = \frac{2 + 6}{2} = 4 \] To find the y-coordinate of the vertex \( y_v \), you'll need the equation of the parabola. If you have the equation or the y-values, we can determine \( y_v \).
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Smaller x-intercept: This is the smaller of the two x-intercepts you provided. \[ \text{Smaller x-intercept: } (2, 0) \]
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Larger x-intercept: This is the larger of the two x-intercepts you provided. \[ \text{Larger x-intercept: } (6, 0) \]
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Y-intercept: To find the y-intercept, you typically set \( x = 0 \) in the equation of the parabola. Without the equation, we can't find the exact y-intercept.
Please provide additional information about the parabola, such as its equation or a point on the graph, to determine the vertex accurately and to find the y-intercept.
can you make the vertex simpler
Certainly! Let's simplify the explanation for finding the vertex of the parabola with x-intercepts at 2 and 6:
- Vertex: The vertex is the midpoint between the x-intercepts. You can find it by taking the average of the two x-intercepts: \[ \text{Vertex } x\text{-coordinate} = \frac{2 + 6}{2} = 4 \] So, the x-coordinate of the vertex is 4.
To find the y-coordinate of the vertex, we would need the equation of the parabola. Without that, we can't provide the exact y-coordinate, but we know the vertex is located at \( (4, y) \).
So, simply put:
- Vertex: \( (4, y) \) (you can find \( y \) if you have the equation)
If you have the equation of the parabola or the position of the curve, I can help you determine \( y \).
Would you like to provide additional information?
y -6
Great! If the y-coordinate of the vertex is -6, we can now specify the vertex of the parabola clearly.
Based on the information you've provided, here are the key features of the parabola:
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Vertex: \[ (4, -6) \]
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Smaller x-intercept: \[ (2, 0) \]
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Larger x-intercept: \[ (6, 0) \]
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Y-intercept: To find the y-intercept, you typically substitute \( x = 0 \) into the equation of the parabola. If the equation of the parabola was derived from the x-intercepts and the vertex, it might be something like \( y = a(x - 2)(x - 6) \).
From what we know, let's summarize:
- Vertex: \( (4, -6) \)
- Smaller x-intercept: \( (2, 0) \)
- Larger x-intercept: \( (6, 0) \)
- Y-intercept: You would need to calculate or provide the value here.
If you have the equation of the parabola or additional details, we can determine the y-intercept. If not, that's fine as we've laid out the key features!