document.write( "Question 1194305: Determine the quadratic function that has the given roots and passes through the given point. Express each function in standard form. (10 marks: 5 marks each) a) x = 2 ± √5, (2, 10) \n" ); document.write( "

Algebra.Com's Answer #826488 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "An alternative path to the answer is using Vieta's theorem with the two given roots.

\n" ); document.write( "The sum of the given roots is 4; the product is -1. So the function is of the form

\n" ); document.write( " $\"y=a%28x%5E2-4x-1%29\"$

\n" ); document.write( "The constant a is determined by the given point.

\n" ); document.write( " $\"10=a%284-8-1%29\"$
\n" ); document.write( " $\"10=-5a\"$
\n" ); document.write( " $\"a=-2\"$

\n" ); document.write( "ANSWER: The function is $\"y=-2%28x%5E2-4x-1%29\"$ or $\"y=-2x%5E2%2B8x%2B2\"$

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