Chapter 3: Q. 3 (page 175)

Graph $f (x) = {(x - 3)}^{2} - 2$ using transformations.

Short Answer

Expert verified

The required graph is

Step by step solution

Step 1. Given information.

Graph $f (x) = {(x - 3)}^{2} - 2$ using transformations.

Step 2. Determine the horizontal and vertical shift.

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

$f (x) = {(x - 3)}^{2} - 2 f (x) = a {(x - h)}^{2} + k S o, h = 3 k = - 2 a = 1$

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 3 units rights to plot $f (x) = {(x - 3)}^{2}$ .

Step 5. Vertical shift of the graph.

Shift the graph of $f (x) = {(x - 3)}^{2}$ to 2 units down to plot $f (x) = {(x - 3)}^{2} - 2$ .

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Graph $f (x) = {(x - 3)}^{2} - 2$ using transformations.

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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Graph f(x)=x-32-2using transformations.

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

Decision Maths

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Study anywhere. Anytime. Across all devices.

Graph $f (x) = {(x - 3)}^{2} - 2$ using transformations.