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Chapter 6: Q. 6 (page 437)

Use transformations to graph the functiony=(x-3)2+2.

Short Answer

Expert verified

The graph of the function is:

Step by step solution

01

Step 1. Given Information

The given function is y=(x-3)2+2and we need to use transformations to graph the function.

02

Step 2. Simplifying the equation

The equation can be written as:

y=(x-3)2+2鈬�y-2=(x-3)2

Using the transformations we get,

X鈮�(x-3)Y鈮�(y-2)鈭�Y=X2

03

Step 3. Finding the vertex 

Comparing the equation with the standard formula of parabola x2=4aywe get,

Vertex of the parabola Y=X2is X=0,Y=0.

鈭�x-3=0鈬�x=3y-2=0鈬�y=2

Vertex of the parabola is(3,2).

04

Step 4. Finding focus of parabola

Focus of the standard parabola is (0,a).

鈭�4a=1鈬�a=14

Transforming we get,

x-3=0鈬�x=3y-2=14鈬�y=2+14鈬�y=94

The focus of the parabola is3,94.

05

Step 5. Graphing the function

The graph of the function is:

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