Chapter 3: Q. 15 (page 155)

Match each graph to one the following functions.
$f (x) = x^{2} - 2 x + 2$

Short Answer

Expert verified

The required graph is in option G.

Step by step solution

Step 1. Write given function in vertex form.

The given function is:

$f (x) = x^{2} - 2 x + 2$

It can be written as:

$f (x) = (x^{2} - 2 x + 1) + 1 f (x) = (x - 1)^{2} + 1 [∵ (a - b)^{2} = a^{2} - 2 a b + b^{2}]$

Step 2. Identify the graph of the function.

The vertex of the function $f (x) = a (x - h)^{2} + k$ is $(h, k)$ . The graph opens up if $a > 0$ and it opens down if $a < 0$ .

In the given function $a = 1, h = 1, k = 1$ . So, the graph must be an upward parabola with vertex at $(1, 1)$ .

Step 3. Conclusion.

The required graph is in option G.

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x	$y = f (x)$
-2	-4
-1	-3.5
0	-3
1	-2.5
2	-2

Match each graph to one the following functions.
$f (x) = x^{2} - 2 x + 2$

Short Answer

Step by step solution

Step 1. Write given function in vertex form.

Step 2. Identify the graph of the function.

Step 3. Conclusion.

One App. One Place for Learning.

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Match each graph to one the following functions.f(x)=x2-2x+2

Short Answer

Step by step solution

Step 1. Write given function in vertex form.

Step 2. Identify the graph of the function.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Match each graph to one the following functions.
$f (x) = x^{2} - 2 x + 2$