document.write( "Question 1209609: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2. \n" ); document.write( "

Algebra.Com's Answer #849662 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Answer: Anything of the form $\"y+=+a%28x-2%29%28x%2B2%29\"$ where 'a' is a real number
\n" ); document.write( "One example is $\"y+=+5%28x-2%29%28x%2B2%29\"$ where a = 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Explanation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If the quadratic has x = 2 as a root, then x-2 = 0. This leads to (x-2) as a factor.
\n" ); document.write( "x = -2 as a root leads to (x+2) as a factor.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "That explains the $\"%28x-2%29%28x%2B2%29\"$ portion.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It changes to $\"a%28x-2%29%28x%2B2%29\"$ so we can vertically stretch and compress the parabola.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check out this Desmos graph.
\n" ); document.write( "https://www.desmos.com/calculator/bzmy0reizl
\n" ); document.write( "Move the slider around for parameter 'a' so you can see these changes.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Notes:

When a < 0, the parabola opens downward.
When a > 0, the parabola opens upward.
When a = 0, the graph is a flat horizontal line overlapping the x axis.
The portion \"takes the value 0 when x = 2\" is redundant since x = 2 is a root aka x intercept.

\n" ); document.write( "

\n" );