document.write( "Question 879707: The quadratic function f(x)= px^2 + qx + r has f(0)= 35,f(1)=20 and f(2)=11.
\n" ); document.write( "Find the values of the constants p,q,r.\r
\n" ); document.write( "\n" ); document.write( "Express f(x) in the form a(x+b)^2+c. Use your answer to find the smallest value of f(x).\r
\n" ); document.write( "\n" ); document.write( "please help\r
\n" ); document.write( "\n" ); document.write( "thank you
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #530996 by ewatrrr(24785) $\"\"$ $\"About$

You can put this solution on YOUR website!

 
\n" );
document.write( "Hi
\n" );
document.write( "f(x)= px^2 + qx + r has 
\n" );
document.write( "f(0)= 35, r = 35
\n" );
document.write( "f(x)= px^2 + qx + 35
\n" );
document.write( "f(1)=20 and f(2)=11
\n" );
document.write( "plug and play, substituting first x = 1  and then x = 2
\n" );
document.write( "I. 20 = p + q + 35   0r 
\n" );
document.write( "II. 11 = 4p + 2q + 35 0r \r
\n" );
document.write( "\n" );
document.write( " 30 = -2p + -2q   |Multiplying EQ I by (-2) and ADDING Eqs I & II to eliminate q
\n" );
document.write( " -24 = 4p + 2q
\n" );
document.write( "    6 = 2p
\n" );
document.write( "    3 = p   and q  = -18  
\n" );
document.write( "f(x)= 3x^2 -18x + 35 
\n" );
document.write( "f(x)= 3(x-3)^2 - 27 + 35  completing the Square
\n" );
document.write( "f(x)= 3(x-3)^2 +8 \n" );
document.write( "

\n" );