Describe how to obtain the graph of g and f if g(x)=2(x + 2)^{2} - 3, h(x)=2x^{2}, and h(x)=2(x - 3)^{2} + 2

aflacatn 2021-03-08 Answered
Describe how to obtain the graph of g and f if g(x)=2(x + 2)2  3, h(x)=2x2, and h(x)=2(x  3)2 + 2
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Expert Answer

Layton
Answered 2021-03-09 Author has 89 answers

Step 1
Properties of the transformation of the graph:
let y=f(x)=2x2.
1) y=f(x  a) shift right by a unit.
2) y=f(x + a) shift left by a unit.
3) y=f(x) + b shift upward by b units.
4) y=f(x)  b shift downward by b units.
5) y=C × f(x) graph stretched expand vertically if
C > 1 and compressed vertically if
C < 1.
Step 2
a) For graph g(x)=2(x + 2)2  3,
Translate f(x)=2x2 by 2 units left and expand vertically by 2 units then shift it down by 3 units you get
g(x)=2(x + 2)2  3.
b) For graph h(x)=2(x  3)2 + 2
Translate f(x)=2x2 by 3 units left and expand vertically by 2 units then shift it down by 2 units you get
h(x)=2(x  3)2 + 2
The graph of all functions are shown in below:
image

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