document.write( "Question 662633: Determine the quardratic function f whose graph given, the vertex is (3,-4) and (2,-1) \n" ); document.write( "

Algebra.Com's Answer #412426 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
Determine the quardratic function f whose graph given, the vertex is (3,-4) and (2,-1)
\n" ); document.write( "**
\n" ); document.write( "Quadratic functions are equations of parabolas of the standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex, A=multiplier which affects slope or narrowness of the curve.
\n" ); document.write( "equation:
\n" ); document.write( "y=A(x-h)^2+k
\n" ); document.write( "y=A(x-3)^2-4
\n" ); document.write( "plug in coordinates of given point (2,-1) to solve for A
\n" ); document.write( "-1=A(2-3)^2-4
\n" ); document.write( "-1=A(-1)^2-4
\n" ); document.write( "A=3
\n" ); document.write( "equation: y=3(x-3)^2-4
\n" ); document.write( "=3(x^2-6x+9)-4
\n" ); document.write( "=3x^2-18x+27-4
\n" ); document.write( "f(x)=3x^2-18x+23\r
\n" ); document.write( "\n" ); document.write( "see graph below as visual check on the answer:
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E2-18x%2B23%29+\"$ \n" ); document.write( "

\n" );