Chapter 3: Q. 6 (page 174)

In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).
$f (x) = {(x - 2)}^{2} + 2$

Short Answer

Expert verified

The required graph is

Step by step solution

Step 1. Given information.

The given quadratic function is $f (x) = {(x - 2)}^{2} + 2$

Step 2. Determine the horizontal and vertical shift.

Compare the function with $f (x) = {(x - h)}^{2} + k$ and determine $h and k$ .

localid="1646225284855" $f (x) = {(x - 2)}^{2} + 2 f (x) = a {(x - h)}^{2} + k S o, h = 2 k = 2 a = 1$

Step 3. plot the graph of the parent function.

Plot the graph of $f (x) = x^{2}$

Step 4. horizontal shift of the graph

Shift the graph of $f (x) = x^{2}$ to 2 units right to plot $f (x) = {(x - 2)}^{2}$ .

Step 5. vertical shift of the graph.

Shift the graph of $f (x) = {(x - 2)}^{2}$ to 2 units up to plot $f (x) = {(x - 2)}^{2} + 2$ .

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In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).
$f (x) = {(x - 2)}^{2} + 2$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the horizontal and vertical shift.

Step 3. plot the graph of the parent function.

Step 4. horizontal shift of the graph

Step 5. vertical shift of the graph.

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In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).fx=x-22+2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the horizontal and vertical shift.

Step 3. plot the graph of the parent function.

Step 4. horizontal shift of the graph

Step 5. vertical shift of the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).
$f (x) = {(x - 2)}^{2} + 2$