What is the function for the graph shown?

  

Whichgraphshowsthefunctionbelow?y=()(x -1)^2+2
A.
B.
10-
1D-
8
&
B
6
4-
2-
2-
0
0
-4
-2
0
2
4
-4
-2
0
N
4
C.
D.
10
10-
8-
8
6
6
4-
4-
2-
0
0

-6
-4
-2
0
2
4
15
-4
-2
0
2
4
00-

Introduction:
Graphs are an essential tool in mathematics, as they help to interpret, analyze, and evaluate various mathematical functions. Among the different types of graphs, the most common ones to represent functions are the line graph, bar graph, and scatter plot. In this article, we will focus on a specific function and try to determine the graph that best represents it.

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Description:
The function y = (x – 1)^2 + 2 is a quadratic function with a vertex located at point (1, 2). To determine the graph that shows this function, we need to plot several points and connect them to form a smooth curve. In the given data, we have two graphs labeled as A and B that represent the function. Graph A has a wider curve, and its vertex is at (1, 10), while Graph B has a narrower curve, and its vertex is at (1, 6). On the x-axis, the two graphs have the same values (-4, -2, 0, 2, 4). However, on the y-axis, Graph A has higher values than Graph B. Therefore, the graph that best represents the function y = (x – 1)^ 2 + 2 is Graph B.

Objectives:
1. To be able to identify which graph represents a specific function.
2. To understand the relationship between the equation of a function and the shape of its graph.

Learning Outcomes:
By the end of this lesson, the learner should be able to:
1. Identify the graph that represents the function y = (x-1)^2 + 2.
2. Explain how changing the equation of a function affects the shape of its graph.

Header: Mathematics

Explanation:
The objective of this lesson is to teach learners about functions and graphs. Specifically, we will focus on the function y = (x-1)^2 + 2 and its corresponding graph. By the end of this lesson, learners should be able to identify which graph represents the function in question and explain how changes to the equation affect the shape of the graph.

Solution 1:
The graph showing the function y = (x -1)^2+2 is graph B. This can be determined by looking at the vertex and the direction of the U-shape of the parabola. The vertex is at (1,2) which is in the center of the U-shape of the parabola in graph B. Additionally, the U-shape of the parabola opens upwards, which is consistent with the equation being in the form of (x-h)^2 + k where h=1 and k=2.

Solution 2:
To visually analyze the graph of the given function, we can notice that the equation is in the vertex form y=(x-h)^2 + k where the vertex of the parabola is (h,k). Looking at the given graphs, the vertex of a parabola with equation y = (x-1)^2+2 must be at the point (1,2). If we compare this point with the given options, we can notice that only graph B has the vertex located at (1,2). Therefore, the correct answer is graph B.

Suggested Resources/Books:
– “Trigonometry: A Complete Introduction” by Hugh Neill and Rachel Ellis
– “Precalculus: Mathematics for Calculus” by James Stewart, Lothar Redlin, and Saleem Watson
– “Calculus: Early Transcendentals” by James Stewart

Similar Asked Questions:
1. What is the standard form of a quadratic equation?
2. How do I find the vertex of a parabola?
3. What is the discriminant of a quadratic equation?
4. How can I use the quadratic formula to solve a quadratic equation?
5. What is the difference between linear and quadratic functions?

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