warm-up, completing the square in #1-2, fill in the missing part of the picture using squares of...
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Warm-Up, Completing the SquareIn #1-2, fill in the missing part of the picture using squares of about this size: to turn the big figure shown into a square.
# of small squares needed: ______ # of small squares needed: ______
1. 2.
In #3-5, factor.
3. x2 + 8x + 16 4. x2 + 6x + 95. x2 - 16x + 64(X+4)2 (X+3)2
(X-8)2
9 16
Warm-Up Part II: Match the Solutions to the Graphs
a. x =-2 or 3 1.
b. x = 4 2.
c. x = {2+i} 3.
d. x = { }
4.5 3
c. (no real solutions)
a. It hits the x-axis at -2 and 3.
b. It hits the x-axis at 4 only.
d. It hits the x-axis at about 3 and 7.
Adapted from resources at: http://webtech.cherokee.k12.ga.us/sequoyah-hs/math/algebra_2_power_point_notes.htm
►Completing the square can be used for non-factorable problems.
►What would make these trinomials perfect squares?
► What do they become in factored form?2) 6 ___c x x 2) 10 ___d x x
2) 4 ___e x x
9 25
42( 3)x 2( 5)x
2( 2)x
Objectives: To create perfect square trinomials. To solve quadratics by
completing the square.
2For a quadratic trinomial ,x bx c
22
2
b
bxx
2
2
bx
Find half the coefficient of the middle term and square it.
So, it factors into this!
You have created a perfect square trinomial (PST).
Completing the Square
23
2
4
9
2
2
3
x
4
932 xx
Write the expression in factored form, then find the value that
makes this expression a perfect square trinomial.
f) x2-3x+___
Complete the square to solve.
g) x2+6x-8=0x2+6x=8x2+6x+___=8+___
(x+3)2
17 3 x
173x
1. Move the constant to the other side.
2. Divide all terms by the leading coefficient (the number with x2).
3. Create a blank on each side.
4. Complete the square.
• Find half the coefficient of the x (middle) term.
• Use that number to rewrite the trinomial as a perfect square.
• Square the number you found.
• Fill that value into each blank.
5. Solve for x.
• Start by square rooting each side.
9 96
3 2
2 2
9
= 17
3 3
►h) 5x2-10x+30=0x2-2x+6=0x2-2x+__=-6+__
(x-1)2
►j) 3x2-12x-24=0x2-4x-8=0x2-4x+__=8+__
(x-2)2
112
2
22
22
b
51 x
51 ix
422
4
22
22
b
2 12x
2 2 3x
You cannot have a leading coefficient!
1 1 4 4
=-5 =12
What if it doesn’t divide out so easily?
k) 3x2+8x+16=0
3x2+8x = -16
21
2b
16
916
9
24
3x
21 8
2 3
24
3
16
9
Still divide by the leading coefficient!
16_____
3
2 8___
3x x
32
9
…continued 24 32
3 9x
4 32
3 9x
4 4 2
3 3
ix
4 4 2
3
ix
SOLVE: Square root
both sides. Simplify. Get x alone.