Sketch the graph of f(x) = -(x-3)2  + 4 using standard transformation techniques.

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter9: Quadratic Equations And Functions
Section9.7: Graph Quadratic Functions Using Transformations
Problem 9.119TI: Graph f(x)=x2+2x3 by using transformations.
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Sketch the graph of f(x) = -(x-3) + 4 using standard transformation techniques.

Expert Solution
Step 1

Suppose the basic function is y=x2

Now,

The graph is 

Calculus homework question answer, step 1, image 1

Step 2

Now,

Reflect the graph of y over the x-axis.

The graph formed is y=-x2

Calculus homework question answer, step 2, image 1

 

Now,

Translate the graph horizontally right by 3 units.

The function graph formed is y=-x-32

Calculus homework question answer, step 2, image 2

 

Now,

Shift the graph vertically up by 4 units.

The function graph formed is y=-x-32+4

Calculus homework question answer, step 2, image 3

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