Christeena & Mathi

P - 5 3/14/13 Solving Quadratic Equations 1) Put equation in

standard form. A rectangular picture has a width that is two-thirds it's length. The picture has an area of 294 inches. What are the dimensions of the picture? Choice 1: 1) Put equation in standard form

and identify a, b, c. Choice 2: Completing The Square Choice 3: Graphing The Equation L = 21

4 = 14 Factoring A process by which the factors

of a composite number

are determined. 2n^2-n-4=2 2n^2-n-6=0 +4= +4 2) Factor Expression. 3) Set each to zero. (2n+3) (n-2)=0 4) Solve each. 2n+3=0 and n-2=0 -3= -3 +2= +2 2n/2= -3/2 or n= 2 2 or -3/2 Using the Quadratic Formula a= 2

b= -1

c= -6 1) 2n2-n-4= 2 -2 = -2 2n2-n-6= 0 2) Calculate value of 4(a)(c) 2) 4(a)(c)= 4(2)(-6)= -48 3) Formula: x= -b +- √b^2-4(a)(c) 2(a) 4) Substitute and tidy up signs. 4) -(-1) +- √(-1)^2 - (-48) 2(2) = 1 +- √1+48 4 = 1 +- √49 4 5) Simplify square root and split plus-or-minus. 5 ) 1+- 7 4 = 1+7 4 and 1-7 4 6) Calculate each. 6) 8/4 or -6/4 = 2 or -3/2 1) Put equation in standard form. 1) 2n^2-n-4= 2 +4 +4 2n^2-n= 6 2) Divide everything by coefficient of a. 2n^2-n= 6 2 2 = n^2-1/2= 3 3) Divide b by 2 and square the value. b= -1/2 (b/2)^2= [(-1/2)/2]^2= -1/2 x 1/2= (-1/4)^2= 1/16 Choice 4: n^2-1/2n+1/16= 3+1/16 (n-1/4)^2 = 48/16 + 1/16 √(n-1/4)^2 = √49/16 n - 1/4 = +- 7/4 +1/4 +1/4 n= 1/4 +- 7/4 Completing the square is the process of

converting quadratic equation into a

perfect square trinomial by adding or

subtracting terms on both sides. 1/4 + 7/4 And 1/4 - 7/4 8/4= 2 and -6/4= -3/2 Bonus Problem 2n^2 -6 -12 1 3 -4 3n -4n -2 n 2n 3

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# Solving Quadratic Equations

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