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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(y3)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— iiié“ 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'
(ErY“
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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 Fall '11
 JimCotter

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