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.

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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?

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