What is the equation of the function shown in the graph?

  

Whichgraph showsthegraphofthefunctionbelow?y=(x- 2)^2+4
A.
B.
9H
8
7
6
5
4
3
2-
1
0
-3-2-1-01 2 3 4 5 6 7
5
4
3
2
1
2 -8 -7 -8 -5-4-3-2-1-01 2
C.
D.
5
4-
B
+ 1
5
4-
3-
2-
1
| 4 -3 -2
0 1 2 3 A 5 6 7
B -7 -6 -5 -4 -3 -2 -14
01 2 3
-2
-3
-4-
-5
3
-4-
-5

Introduction:
Graphs are an effective way of visualizing functions that help identify their behavior. When plotting a function with mathematical expression, it is essential to understand the curve’s shape and interpret it correctly. In this context, we will examine a particular function and determine the graph that represents it.

Don't use plagiarized sources. Get Your Custom Essay on
What is the equation of the function shown in the graph?
Just from $13/Page
Order Essay

Description:
Consider the function y=(x- 2)^2+4. In the given data, four graphs are shown to represent the function. Our primary task is to find out which graph is the correct representation of the function. Graph A and C are clearly not the correct choices since they are vertical lines, whereas the given function is quadratic. Graph D, on the other hand, represents a negative quadratic function, which does not match the original expression’s form. That leaves us with graph B, which is a parabolic curve that opens upwards. Therefore, the correct graph that represents the given function is graph B.

Objectives:

– To understand how to graph a quadratic function
– To identify the equation of a quadratic function given its graph
– To determine the vertex and axis of symmetry of a quadratic function

Learning Outcomes:

By the end of this lesson, learners will be able to:

– Identify the graph of a quadratic function y=(x-2)^2+4 among the four given graphs.
– Determine the vertex and axis of symmetry of a quadratic function from its graph.
– Sketch the graph of a quadratic function given its equation in the vertex form y=a(x-h)^2+k.
– Solve problems involving quadratic functions and their graphs, such as finding maximum and minimum values and intercepts.

Solution 1:

Based on the given equation, y=(x-2)^2 + 4, we can identify that the function represents a parabola. The vertex of the parabola is at the point (2, 4). The minimum value of the function is 4, which is the y-intercept of the parabola.

The graph of the function can be identified as graph A. Graph A shows a parabola with a vertex at (2, 4) and opens upwards.

Solution 2:

To identify the graph of the function y=(x-2)^2 + 4, we can start by analyzing the properties of the equation. The equation describes a parabola with a vertex at (2, 4) and opens upwards.

Looking at the given graphs, we can see that the graph that matches this description is graph A. Graph A shows a parabola that opens upwards and has a vertex at (2, 4). Therefore, the graph of the function y=(x-2)^2 + 4 is represented by graph A.

Suggested Resources/Books:
1. “Calculus: Early Transcendentals” by James Stewart
2. “Functions and Graphs” by I.M. Gelfand and E.G. Glagoleva
3. “Precalculus: A Prelude to Calculus” by Sheldon Axler and Kent Staley

Similar asked questions:
1. What is the vertex form of the quadratic function?
2. How do you find the axis of symmetry of a parabola?
3. How do you find the maximum or minimum value of a quadratic equation?
4. How do you graph a quadratic function?
5. What is the significance of the discriminant in quadratic equations?

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
× How can I help you?