Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Writing Equations from Quadratic Graphs
**Task:** Write an equation (any form) for the quadratic graphed below:
**Graph Details:**
- The graph depicts a quadratic function, showing a parabolic curve opening downwards.
- The vertex of the parabola is at the point (2, 2).
- The parabola intersects the x-axis at approximately (0,0) and (4,0).
- The y-axis ranges from -5 to 5.
- The x-axis ranges from -5 to 5.
**How to Determine the Equation:**
1. **Identify Key Features:**
- Vertex (h, k): (2, 2)
- X-intercepts: (0, 0) and (4, 0)
2. **Using Vertex Form of a Quadratic Function:**
The vertex form of a quadratic equation is given by:
\[
y = a(x - h)^2 + k
\]
Substituting the vertex (2, 2):
\[
y = a(x - 2)^2 + 2
\]
3. **Determine 'a' Using Another Point:**
Use one of the x-intercepts, say (0, 0), to find the value of 'a'.
\[
0 = a(0 - 2)^2 + 2
\]
\[
0 = 4a + 2
\]
\[
-2 = 4a
\]
\[
a = -\frac{1}{2}
\]
4. **Write the Final Equation:**
\[
y = -\frac{1}{2}(x - 2)^2 + 2
\]
**Conclusion:**
The equation of the quadratic graph is:
\[
y = -\frac{1}{2}(x - 2)^2 + 2
\]
Please enter the equation in the box provided:
```
y = [ ]
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2cfdfc8-ec6f-4853-bb37-f02ea76b87be%2F40d9591e-b96a-4847-add7-220aa8b2ff62%2Fon99t6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Writing Equations from Quadratic Graphs
**Task:** Write an equation (any form) for the quadratic graphed below:
**Graph Details:**
- The graph depicts a quadratic function, showing a parabolic curve opening downwards.
- The vertex of the parabola is at the point (2, 2).
- The parabola intersects the x-axis at approximately (0,0) and (4,0).
- The y-axis ranges from -5 to 5.
- The x-axis ranges from -5 to 5.
**How to Determine the Equation:**
1. **Identify Key Features:**
- Vertex (h, k): (2, 2)
- X-intercepts: (0, 0) and (4, 0)
2. **Using Vertex Form of a Quadratic Function:**
The vertex form of a quadratic equation is given by:
\[
y = a(x - h)^2 + k
\]
Substituting the vertex (2, 2):
\[
y = a(x - 2)^2 + 2
\]
3. **Determine 'a' Using Another Point:**
Use one of the x-intercepts, say (0, 0), to find the value of 'a'.
\[
0 = a(0 - 2)^2 + 2
\]
\[
0 = 4a + 2
\]
\[
-2 = 4a
\]
\[
a = -\frac{1}{2}
\]
4. **Write the Final Equation:**
\[
y = -\frac{1}{2}(x - 2)^2 + 2
\]
**Conclusion:**
The equation of the quadratic graph is:
\[
y = -\frac{1}{2}(x - 2)^2 + 2
\]
Please enter the equation in the box provided:
```
y = [ ]
```
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