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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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

Layton · Accepted Answer

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 &amp;gt; 1 and compressed vertically if C &amp;lt; 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:

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

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