document.write( "Question 121328: A quadratic function has x-intercepts at (-8,0) and (2,0). What is the transformational form of the function if the minimum y value is -3?
\n" ); document.write( "a) y=3/25(x+3)^2-3
\n" ); document.write( "b) 25/3(y+3)=(x+3)^2
\n" ); document.write( "c) 25/3(y-3)=(x-3)^2
\n" ); document.write( "d) 3/25(y-3)=(x-3)^2 \n" ); document.write( "

Algebra.Com's Answer #89057 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
A quadratic function has x-intercepts at (-8,0) and (2,0).
\n" ); document.write( "What is the transformational form of the function if the
\n" ); document.write( "minimum y value is -3?
\n" ); document.write( "a) y=3/25(x+3)^2-3
\n" ); document.write( "b) 25/3(y+3)=(x+3)^2
\n" ); document.write( "c) 25/3(y-3)=(x-3)^2
\n" ); document.write( "d) 3/25(y-3)=(x-3)^2
\n" ); document.write( "

\r\n" );
document.write( "Since it has intercepts (-8,0) and (2,0), the axis of\r\n" );
document.write( "symmetry must pass through their midpoint, which is \r\n" );
document.write( "\r\n" );
document.write( "(,) or (,) = (-3,0)\r\n" );
document.write( "\r\n" );
document.write( "The axis of symmetry has equation x = h, which is x = -3 \r\n" );
document.write( "\r\n" );
document.write( "The vertex then must be (h,k) where h = -3 and k is the \r\n" );
document.write( "minimum y value, which is -3.\r\n" );
document.write( "\r\n" );
document.write( "The equation of a parabola is\r\n" );
document.write( "\r\n" );
document.write( "   c(y-k) = (x-h)^2\r\n" );
document.write( "\r\n" );
document.write( "c(y-(-3)) = (x-(-3))^2\r\n" );
document.write( "\r\n" );
document.write( "   c(y+3) = (x+3)^2\r\n" );
document.write( "\r\n" );
document.write( "Since the parabola passes through (2,0)\r\n" );
document.write( "\r\n" );
document.write( "   c(0+3) = (2+3)^2\r\n" );
document.write( "       3c = 5^2\r\n" );
document.write( "       3c = 25\r\n" );
document.write( "        c = 25/3\r\n" );
document.write( "\r\n" );
document.write( "So  \r\n" );
document.write( "\r\n" );
document.write( "   c(y+3) = (x+3)^2\r\n" );
document.write( "\r\n" );
document.write( "is now\r\n" );
document.write( "\r\n" );
document.write( "   (y+3) = (x+3)^2\r\n" );
document.write( "\r\n" );
document.write( "So the answer is (b)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );