Pergunta
Use transformations of the graph of f(x)=x^2 to determine the graph of the given function. g(x)=4(x-2)^2 Select all the transformations that are needed to graph the given function using f(x)=x^2 A. Shift the graph 2 units up B. Reflect the graph about the x-axis. C. Reflect the graph about the y-axis. D. Stretch the graph horizontally by a factor of 4 E. Shrink the graph vertically by a factor of 4 F. Stretch the graph vertically by a factor of 4 G. Shrink the graph horizontally by a factor of 4.
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LuizMestre · Tutor por 5 anos
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To determine the transformations needed to graph the function $g(x)=4(x-2)^{2}$ using the graph of $f(x)=x^{2}$, we can compare the given function with the standard form of a quadratic function, which is $a(x-h)^{2}+k$, where $(h,k)$ represents the vertex of the parabola.<br /><br />Comparing $g(x)=4(x-2)^{2}$ with the standard form, we can see that:<br />- The coefficient 4 in front of $(x-2)^{2}$ indicates a vertical stretch by a factor of 4.<br />- The term $(x-2)$ inside the squared parentheses indicates a horizontal shift 2 units to the right.<br />- There is no constant term added or subtracted outside the squared parentheses, so there is no vertical shift.<br /><br />Therefore, the transformations needed to graph the function $g(x)=4(x-2)^{2}$ using $f(x)=x^{2}$ are:<br />- Shift the graph 2 units to the right (option D)<br />- Stretch the graph vertically by a factor of 4 (option F)<br /><br />So, the correct options are D and F.
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