document.write( "Question 856847: Hi, could i please have some help with this question, thank you in advance.\r
\n" ); document.write( "\n" ); document.write( "Write a paragraph explaining how a quadratic function can be graphed by applying transformations to $\"f%28x%29=x%5E2\"$ . Fill in the blanks below.
\n" ); document.write( "The graph of a quadratic function $\"g%28x%29=a%28x-h%29%5E2%2Bk\"$ can be plotted from the function $\"f%28x%29=x%5E2\"$ by applying transformation properties.
\n" ); document.write( "- The parameter a _____________________________________________.
\n" ); document.write( "- The parameter h affects the ______________________________ translation and moves the graph to the right if __________ and to the left if __________.
\n" ); document.write( "- The parameter k affects the ______________________________ translation and moves the graph up if _________________ and down if ______________.
\n" ); document.write( "- The vertex is located at ________________________________________.
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Algebra.Com's Answer #516169 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
The trickiest part to learn at first is what happens when you add or subtract a value to x. You already know that the vertex of $\"f%28x%29=x%5E2\"$ is at (0,0). If you change to $\"f%28x%29=%28x-3%29%5E2\"$ , then you want to know where does the vertex and the rest of the graph go? Consider x=3. This makes $\"f%28x%29=%283-3%29%5E2=0%5E2=0\"$ . No change has been done to y, only changed was in x. We moved x three units rightward when we SUBTRACTED 3 from independent variable x.\r
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\n" ); document.write( "\n" ); document.write( "(Here, h is assumed a positive number): That is a representative example to show that $\"f%28x%29=%28x-h%29%5E2\"$ is the same shape as $\"f%28x%29=x%5E2\"$ but moved h units to the right. Pay attention to the operation symbol used. $\"%28x%2Bh%29%5E2\"$ is the same as $\"%28x-%28-h%29%29%5E2\"$ and this would represent, if h itself were a positive number, h units movement to the LEFT. \r
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\n" ); document.write( "\n" ); document.write( "The factor, a, shrinks the graph vertically if $\"abs%28a%29%3C1\"$ , but stretches the graph vertically if $\"abs%28a%29%3E1\"$ . \n" ); document.write( "

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