11.1 - CHAPTER 11 QUADRATIC EQUATIONS AND FUNCTIONS 11.1...

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Unformatted text preview: CHAPTER 11 QUADRATIC EQUATIONS AND FUNCTIONS 11.1 SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE Sguare Root Propem We previously have used factoring to solve quadratic equations. This chapter will introduce additional methods for solving quadratic equations. If I) is a real number and a2 = b, then a =tJB. Solve x2 = 49 X :4: 3L Solve 2x2 = 4 x : + K} is 501V8(y-3)2=4 H ,g) .7: a L J '33 -: f Ll ‘nd g t; t at LJ~7> t Solvexz+4=0 3 Solve(3x—17)2=28 F. X :_ 1:} pad; L21, Pa Bx—H: ths 3 ’ 3 3X : ITI— iii-é“ Completing the Sguare We now look at a method for solving quadratics that involves a technique called completing the square. It involves creating a trinomial that is a perfect square, setting the factored trinomial equal to a constant, then using the square root property from the previous section. Solving a Quadratic Equation in x by Completing the Square 1) If the coefficient of x2 is 1, go to Step 2. Otherwise, divide both sides of the equation by the coefficient of 162' 2) Isolate all variable terms on one side of the equation. 3) Complete the square for the resulting binomial by adding the square of half of the coefficient of x to both sides of the equation. 4) Factor the resulting perfect square trinomial and write it as the square of a binomial. 5) Use the square root property to solve for x. Ereliminagy work: What constant term should be added to the following expressions to '2. create a perfect square trinomial? 045—) F i...) (Muse) x: # 10x 4—25 ff XE 5.x ,gx +0.5" 2. ,. z (x ‘5) ("12.) x2: [ox +2? ab" El €531 x2+16x (by; U? (x. 4-?) 2' (Er-Y“ x2—7x+ 31 (X #272); L]. Solve by completing the square. y2+6y.=—8 A, 2. 32. 9 fliétr+ 3...; Pg'lr' C? (3+ 5);: ' 3+3 2 if:— 3+33i| , +3 : “'1 :: ’3 11 ’9 / Solve by completing the square. 2 _ y +y — 7 -— 0 I). 8 + . El . : 4 L Hi) g (x. Lye. Li}; [\ “J l4- EV‘v‘ *‘Hng. (EJYLLGWYQ 7. 51a )(ngilX +8 2: O >£°1 + W “:‘6 3 51 2.1 Lt : Xa+qx+ 4 Z; ——£D+ , (Magi : #a wax: tJ'a X—l—EL: :1in X —; flash N3; (9“) h (- PQI‘LJl Solve by completing the square. 2x2+14x—1=0 I : QKXQfiLF’” “‘3’) D ...
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This note was uploaded on 01/16/2012 for the course MATH 096 taught by Professor Jimcotter during the Fall '11 term at Truckee Meadows Community College.

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11.1 - CHAPTER 11 QUADRATIC EQUATIONS AND FUNCTIONS 11.1...

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