document.write( "Question 463805: A quadratic relation has zeros at -2 and 8, and a y-intercept of 8. Determine the equation of the relation in veertex form \n" ); document.write( "

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A quadratic relation has zeros at -2 and 8, and a y-intercept of 8. Determine the equation of the relation in vertex form
\n" ); document.write( "...
\n" ); document.write( "Standard form for parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
\n" ); document.write( "We have three points to work with: (-2,0),(8,0) and (0,8)
\n" ); document.write( "h=midpoint between -2 and 8=(-2+8)/2=6/2=3
\n" ); document.write( "equation: y=A(x-3)^2+k
\n" ); document.write( "using point (0,8), the y-intercept
\n" ); document.write( "8=A(0-3)^2+k
\n" ); document.write( "8=9A+k
\n" ); document.write( "using point (-2,0), one of the zeros
\n" ); document.write( "0=A(-2-3)^2+k
\n" ); document.write( "0=25A+k
\n" ); document.write( "8=9A+k
\n" ); document.write( "subtract
\n" ); document.write( "-8=16A
\n" ); document.write( "A=-1/2
\n" ); document.write( "k=8-9A=8+4.5=12.5
\n" ); document.write( "Equation:
\n" ); document.write( "y=-.5(x-3)^2+12.5
\n" ); document.write( "see graph below as a visual check on the answer
\n" ); document.write( "..
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-20%2C+20%2C+-.5%28x-3%29%5E2%2B12.5%29+\"$ \n" ); document.write( "

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