document.write( "Question 933106: Kindly help me with parabola question.the x and y intercept of a quadratic function in the form y=a(x-h)^2+k
\n" ); document.write( "are (2,0),(-4,0)(0,16).solve for a,h and k. \n" ); document.write( "

Algebra.Com's Answer #566625 by MathLover1(20850) $\"\"$ $\"About$

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$\"y=a%28x-h%29%5E2%2Bk\"$ ,Vertex Form, where $\"k=y-intercept\"$ and y-coordinate of the vertex, and $\"h\"$ is x-coordinate of the vertex\r
\n" ); document.write( "\n" ); document.write( "vertex is at (h, k)
\n" ); document.write( "given points:
\n" ); document.write( "( $\"2\"$ , $\"0\"$ ),----> x-intercept
\n" ); document.write( "( $\"-4\"$ , $\"0\"$ )----> x-intercept
\n" ); document.write( "( $\"0\"$ , $\"16\"$ )-> since $\"x=0\"$ , this is y-intercept and $\"highlight%28k=16%29\"$ , then vertex is at (h, 16)\r
\n" ); document.write( "\n" ); document.write( "since
\n" ); document.write( "Vertex:
\n" ); document.write( " $\"x\"$ coordinate of vertex is $\"h\"$ and the x-coordinate of the vertex is halfway between the x-coordinates of the x-intercepts which is the distance from $\"2\"$ to $\"-4\"$ divided by $\"2\"$ : $\"%28-4%2B2%29%2F2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "then $\"highlight%28h=-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, we know that $\"h=-1\"$ and $\"k=16\"$ ; so, the coordinate of the vertex are ( $\"-1\"$ , $\"16\"$ )\r
\n" ); document.write( "\n" ); document.write( "now find $\"a\"$ using one of given points and vertex\r
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\n" ); document.write( "\n" ); document.write( " $\"y=a%28x-h%29%5E2%2Bk\"$ ...use ( $\"2\"$ , $\"0\"$ )-> since $\"y=0\"$ , this is $\"highlight%28x-intercept%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=a%282-%28-1%29%29%5E2%2B16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=a%283%29%5E2%2B16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=9a%2B16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-16=9a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-16%2F9=a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28-16%2F9=a%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, our equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=-%2816%2F9%29%28x%2B1%29%5E2%2B16\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+20%2C+-%2816%2F9%29%28x%2B1%29%5E2%2B16%29+\"$ \r
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