College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.CT: Chapter Test
Problem 6CT: Assume that an object tossed vertically upward reaches a height of h feet after t seconds, where...
Related questions
Topic Video
Question
Please help
![### Write an equation (any form) for the quadratic graphed below
#### Description of the Graph:
The graph displays a parabola that opens downwards. It is positioned on a coordinate plane with the x-axis ranging from -5 to 5 and the y-axis ranging from -5 to 5.
- The vertex of the parabola is at the point (-2, 4).
- The parabola intersects the x-axis at two points: \(x = -5\) and \(x = 1\).
- The y-axis passing through the y-coordinate 0 intersects the parabola at the point \(y = -3\), when \(x = 0\).
#### Diagram Explanation:
The graph plots a quadratic function on a coordinate plane. The highest point of the graph (vertex) is at (-2, 4). This vertex indicates that the function has a maximum value at this point since the graph opens downwards. The width and direction of the parabola are consistent with the standard shape of quadratic graphs.
#### Diagram:
[Here you would include an illustration of the graph similar to the one described above.]
#### Equation (Vertex Form):
Given the vertex form of a quadratic equation:
\[ y = a(x - h)^2 + k \]
Where:
- \( (h, k) \) is the vertex of the parabola
- \( a \) is the leading coefficient that determines the width and direction of the parabola
Since the vertex is at (-2, 4):
\[ y = a(x + 2)^2 + 4 \]
To find the value of \( a \), use another point from the graph. Let's use the point \( (1, 0) \):
\[ 0 = a(1 + 2)^2 + 4 \]
\[ 0 = a(3)^2 + 4 \]
\[ 0 = 9a + 4 \]
\[ -4 = 9a \]
\[ a = -\frac{4}{9} \]
Therefore, the equation in vertex form is:
\[ y = -\frac{4}{9}(x + 2)^2 + 4 \]
#### Question Help:
To further understand how to derive the equation of the parabola, you can watch the following instructional videos for additional guidance:
- Video 1 [Link to video]
- Video 2 [Link to video]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5253470b-a88a-44a2-95c4-a44ae3e11575%2F5a3b77ac-2926-43e0-a57e-614b4e06ddcc%2Fs7hnod_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Write an equation (any form) for the quadratic graphed below
#### Description of the Graph:
The graph displays a parabola that opens downwards. It is positioned on a coordinate plane with the x-axis ranging from -5 to 5 and the y-axis ranging from -5 to 5.
- The vertex of the parabola is at the point (-2, 4).
- The parabola intersects the x-axis at two points: \(x = -5\) and \(x = 1\).
- The y-axis passing through the y-coordinate 0 intersects the parabola at the point \(y = -3\), when \(x = 0\).
#### Diagram Explanation:
The graph plots a quadratic function on a coordinate plane. The highest point of the graph (vertex) is at (-2, 4). This vertex indicates that the function has a maximum value at this point since the graph opens downwards. The width and direction of the parabola are consistent with the standard shape of quadratic graphs.
#### Diagram:
[Here you would include an illustration of the graph similar to the one described above.]
#### Equation (Vertex Form):
Given the vertex form of a quadratic equation:
\[ y = a(x - h)^2 + k \]
Where:
- \( (h, k) \) is the vertex of the parabola
- \( a \) is the leading coefficient that determines the width and direction of the parabola
Since the vertex is at (-2, 4):
\[ y = a(x + 2)^2 + 4 \]
To find the value of \( a \), use another point from the graph. Let's use the point \( (1, 0) \):
\[ 0 = a(1 + 2)^2 + 4 \]
\[ 0 = a(3)^2 + 4 \]
\[ 0 = 9a + 4 \]
\[ -4 = 9a \]
\[ a = -\frac{4}{9} \]
Therefore, the equation in vertex form is:
\[ y = -\frac{4}{9}(x + 2)^2 + 4 \]
#### Question Help:
To further understand how to derive the equation of the parabola, you can watch the following instructional videos for additional guidance:
- Video 1 [Link to video]
- Video 2 [Link to video]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University