# 1b-2_Completing_the_square.docx - Completing the square A...

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Completing the squareA LEVEL LINKSScheme of work:1b. Quadratic functions – factorising, solving, graphs and the discriminantsKey pointsCompleting the square for a quadratic rearrangesax2+bx+cinto the formp(x+q)2+rIfa≠ 1, then factorise usingaas a common factor.ExamplesExample 1Complete the square for the quadratic expressionx2+ 6x− 2x2+ 6x− 2= (x+ 3)2− 9 − 2= (x+ 3)2− 111Writex2+bx+cin the form2222bbxc2SimplifyExample 2Write 2x2− 5x+ 1 in the formp(x+q)2+r2x2− 5x+ 1=25212xx=22552144x=25252148x=2517248x1Before completing the square writeax2+bx+cin the form2baxxca2Now complete the square by writing252xxin the form2222bbx3Expand the square brackets – don’tforget to multiply254by thefactor of 24Simplify
Practice1Write the following quadratic expressions in the form (x+p)2+ax2+ 4x+ 3bx2– 10x– 3cx2– 8xdx2+ 6xex2– 2x+ 7fx2+ 3q
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