document.write( "Question 972032: Determine the equation of parabola which has turning point (3;4) and passes trough the point (4;2) \n" ); document.write( "

Algebra.Com's Answer #594441 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
parabolas are symmetric around the vertex x-value. From (3,4) to (4,2) is one point; another is (2,2) The vertex is higher than the point, so this is convex upward, and a will be negative. \r
\n" ); document.write( "\n" ); document.write( "Vertex form of a parabola is a (x-h)^2 +k ; h is 3 and k is 4
\n" ); document.write( "a (x-3)^2 + 4=y\r
\n" ); document.write( "\n" ); document.write( "substitute for x and y
\n" ); document.write( "a(4-3)^2+4=2 ; a(2-3)^2 +4=2\r
\n" ); document.write( "\n" ); document.write( "a +4=-2 ; a=-2;;;; a+4=2, a= -2\r
\n" ); document.write( "\n" ); document.write( "y=-2(x-3)^2 +4 = -2(x^2-6x+9)+4
\n" ); document.write( "y= -2x^2 +12x -14,
\n" ); document.write( "Check: vertex x-value should be -b/2a; -12/-4 =3. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C-2x%5E2%2B12x-14%29\"$ \n" ); document.write( "

\n" );