document.write( "Question 355341: A quadratic function has an axis of symmetry of x=4, a y-intercept of 33 and also passes through the point, P(5,3). Write the equation of this function in the form of y=ax^2+bx+c. \n" ); document.write( "

Algebra.Com's Answer #253841 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
A quadratic function has an axis of symmetry of x=4, a y-intercept of 33 and also passes through the point, P(5,3). Write the equation of this function in the form of y=ax^2+bx+c.
\n" ); document.write( "

\r\n" );
document.write( "Let's draw what we have,  Since its y-intercept is 33, it passes\r\n" );
document.write( "through the point (0,33). We will draw its axis of symmetry and plot\r\n" );
document.write( "the points (0,33) and (5,3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the line x=4 is the axis of symmetry and since the point\r\n" );
document.write( "(5,3) is on the graph, its reflection across the line x=4 is\r\n" );
document.write( "also a point on the graph.  That point is (3,3).  Also the\r\n" );
document.write( "reflection of the y-intercept (0,33) across the line of symmetry \r\n" );
document.write( "is also a point on the graph.  That point is (8,33).  So we have \r\n" );
document.write( "four points on the parabola and we only need three.\r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we pick any three of the four points and substitute them in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substituting in (0,33)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we already have c=33:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substituting (8,33) in that\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substituting (3,3) in that\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve that system and get a=2 and b=-16\r\n" );
document.write( "\r\n" );
document.write( "So the parabola's equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and here is its graph: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );