Question
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5 of 95 of 9 Items
Question 1
Directions:
Answer the questions below.
You will be able to check your answers by clicking on "Check Answers" at the bottom.
Check your answers as you work.
Treat this like a test review
We encourage you to score at least 70% before submitting so you feel prepared for your unit test.
Label the key parts of the parabola.
(1 point)
response - correct
Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.vertexSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.zeroSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.zeroSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.line of symmetry
Question 2
Identify the key parts of this parabola(1 point)
A) The vertex is
(write your response as an ordered pair).
B) The lesser zero is
(write your response as an ordered pair)
C) The other zero is
(write your response as an ordered pair)
D) The line of symmetry is
(write your response as an equation)
E) The y-intercept is
(write your response as an ordered pair)
F) Complete the table below
5 of 95 of 9 Items
Question 1
Directions:
Answer the questions below.
You will be able to check your answers by clicking on "Check Answers" at the bottom.
Check your answers as you work.
Treat this like a test review
We encourage you to score at least 70% before submitting so you feel prepared for your unit test.
Label the key parts of the parabola.
(1 point)
response - correct
Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.vertexSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.zeroSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.zeroSelect responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.line of symmetry
Question 2
Identify the key parts of this parabola(1 point)
A) The vertex is
(write your response as an ordered pair).
B) The lesser zero is
(write your response as an ordered pair)
C) The other zero is
(write your response as an ordered pair)
D) The line of symmetry is
(write your response as an equation)
E) The y-intercept is
(write your response as an ordered pair)
F) Complete the table below
Answers
GPT-4o mini
To help you with the questions related to the parabola, I would need additional information or context regarding the specific parabola you're analyzing. However, I can provide you with a general approach on how to find and label the key parts of a parabola.
Let's break it down step by step:
### Key Parts of a Parabola
1. **Vertex**: The highest or lowest point of the parabola, depending on whether it opens upwards or downwards. If the parabola is given in standard form \(y = ax^2 + bx + c\), you can find the vertex using the vertex formula:
\[
x = -\frac{b}{2a}
\]
Then, substitute this value back into the equation to find the y-coordinate of the vertex.
2. **Zeros (Roots)**: These are the x-values where the parabola intersects the x-axis. You can find them by solving the equation \(ax^2 + bx + c = 0\) using factoring, the quadratic formula, or by graphing.
3. **Line of Symmetry**: This is a vertical line that passes through the vertex. Its equation can be found using the x-coordinate of the vertex:
\[
x = -\frac{b}{2a}
\]
4. **Y-Intercept**: This is the point where the parabola intersects the y-axis. It can be found by evaluating the function when \(x = 0\) (i.e., \(y = c\)).
### Example of Labeling Key Parts:
Suppose you have a parabola described by the equation:
\[ y = 2x^2 - 8x + 6 \]
**A) The vertex**:
- Calculate the vertex:
- \(a = 2, b = -8\)
- \(x = -\frac{-8}{2 \cdot 2} = 2\)
- Substitute \(x = 2\) into the equation:
\[
y = 2(2)^2 - 8(2) + 6 = 8 - 16 + 6 = -2
\]
- Vertex: \( (2, -2) \)
**B) The lesser zero**:
- Use the quadratic formula to find zeros:
\[
x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}
\]
- Calculate the discriminant and find the roots.
**C) The other zero**:
- This will also be calculated in the same step as the lesser zero.
**D) The line of symmetry**:
- From the vertex, \(x = 2\).
**E) The y-intercept**:
- Substitute \(x = 0\) into the equation:
\[
y = 6
\]
- Y-intercept: \( (0, 6) \)
### Completing the Table
Create a table with the identified key parts:
| Key Part | Value |
|-------------------|-------------------|
| Vertex | (2, -2) |
| Lesser Zero | Example point |
| Other Zero | Example point |
| Line of Symmetry | x = 2 |
| Y-Intercept | (0, 6) |
If you provide the specific equation of the parabola, I can assist you further with exact calculations!
Let's break it down step by step:
### Key Parts of a Parabola
1. **Vertex**: The highest or lowest point of the parabola, depending on whether it opens upwards or downwards. If the parabola is given in standard form \(y = ax^2 + bx + c\), you can find the vertex using the vertex formula:
\[
x = -\frac{b}{2a}
\]
Then, substitute this value back into the equation to find the y-coordinate of the vertex.
2. **Zeros (Roots)**: These are the x-values where the parabola intersects the x-axis. You can find them by solving the equation \(ax^2 + bx + c = 0\) using factoring, the quadratic formula, or by graphing.
3. **Line of Symmetry**: This is a vertical line that passes through the vertex. Its equation can be found using the x-coordinate of the vertex:
\[
x = -\frac{b}{2a}
\]
4. **Y-Intercept**: This is the point where the parabola intersects the y-axis. It can be found by evaluating the function when \(x = 0\) (i.e., \(y = c\)).
### Example of Labeling Key Parts:
Suppose you have a parabola described by the equation:
\[ y = 2x^2 - 8x + 6 \]
**A) The vertex**:
- Calculate the vertex:
- \(a = 2, b = -8\)
- \(x = -\frac{-8}{2 \cdot 2} = 2\)
- Substitute \(x = 2\) into the equation:
\[
y = 2(2)^2 - 8(2) + 6 = 8 - 16 + 6 = -2
\]
- Vertex: \( (2, -2) \)
**B) The lesser zero**:
- Use the quadratic formula to find zeros:
\[
x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}
\]
- Calculate the discriminant and find the roots.
**C) The other zero**:
- This will also be calculated in the same step as the lesser zero.
**D) The line of symmetry**:
- From the vertex, \(x = 2\).
**E) The y-intercept**:
- Substitute \(x = 0\) into the equation:
\[
y = 6
\]
- Y-intercept: \( (0, 6) \)
### Completing the Table
Create a table with the identified key parts:
| Key Part | Value |
|-------------------|-------------------|
| Vertex | (2, -2) |
| Lesser Zero | Example point |
| Other Zero | Example point |
| Line of Symmetry | x = 2 |
| Y-Intercept | (0, 6) |
If you provide the specific equation of the parabola, I can assist you further with exact calculations!