Question
Graphs of Quadratic Equations Quick Check
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Question
Use the image to answer the question.
A parabola is graphed on a coordinate plane. The x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 1 to 16 in increments of 1.
Determine which of the following statements is true about the parabola.
(1 point)
Responses
The y-intercept and the x-intercepts share the same point.
The y -intercept and the x -intercepts share the same point.
The vertex and the x-intercepts share the same point.
The vertex and the x -intercepts share the same point.
There is only one x-intercept.
There is only one x -intercept.
The y-intercept and the vertex share the same point.
The y -intercept and the vertex share the same point.
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Answers
GPT-4o mini
To determine which statement about the parabola is true, we need to analyze the characteristics of a parabola based on its shape and key points such as the vertex, x-intercepts, and y-intercept.
1. **The y-intercept and the x-intercepts share the same point.**
- This is only true if the value that the parabola crosses the y-axis is also one of the x-intercept points. This is generally not true for most parabolas unless they have specific symmetry and location.
2. **The vertex and the x-intercepts share the same point.**
- This statement is only true if the vertex of the parabola lies exactly on the x-axis where it crosses. This typically only occurs in parabolas that are tangent to the x-axis.
3. **There is only one x-intercept.**
- A parabola can have either two x-intercepts, one (if it just touches the x-axis), or none (if it opens above the x-axis). This statement might be true if the parabola is tangent to the x-axis.
4. **The y-intercept and the vertex share the same point.**
- This is only true in specific parabolas where the vertex is positioned directly on the y-axis. It’s not generally true for all parabolas.
Without seeing the specific image of the parabola, determining the truth of the statements is difficult. However, if the parabola only touches the x-axis at its vertex, then the statement "There is only one x-intercept" would be true.
If the parabola clearly has distinct x-intercepts and a y-intercept that is separate from the vertex, the first three statements likely wouldn't hold.
Based on typical options given the nature of most parabolas, the most likely correct statement is **"There is only one x-intercept,"** assuming the parabola is tangent to the x-axis.
Please check the specific graph to confirm which one fits.
1. **The y-intercept and the x-intercepts share the same point.**
- This is only true if the value that the parabola crosses the y-axis is also one of the x-intercept points. This is generally not true for most parabolas unless they have specific symmetry and location.
2. **The vertex and the x-intercepts share the same point.**
- This statement is only true if the vertex of the parabola lies exactly on the x-axis where it crosses. This typically only occurs in parabolas that are tangent to the x-axis.
3. **There is only one x-intercept.**
- A parabola can have either two x-intercepts, one (if it just touches the x-axis), or none (if it opens above the x-axis). This statement might be true if the parabola is tangent to the x-axis.
4. **The y-intercept and the vertex share the same point.**
- This is only true in specific parabolas where the vertex is positioned directly on the y-axis. It’s not generally true for all parabolas.
Without seeing the specific image of the parabola, determining the truth of the statements is difficult. However, if the parabola only touches the x-axis at its vertex, then the statement "There is only one x-intercept" would be true.
If the parabola clearly has distinct x-intercepts and a y-intercept that is separate from the vertex, the first three statements likely wouldn't hold.
Based on typical options given the nature of most parabolas, the most likely correct statement is **"There is only one x-intercept,"** assuming the parabola is tangent to the x-axis.
Please check the specific graph to confirm which one fits.