5.7 Completing the Square Day 2 - Poudre School...
Transcript of 5.7 Completing the Square Day 2 - Poudre School...
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5‐7 Completing the SquareDay 2
Objectives: *Solve equations by completing the square... *Rewrite functions by completing the square...
...when a does not equal one!!!
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Review #1: Find the missing value to complete the square.
x2 ‐ 14x +
( )2 = ( )2 = 49
x2 ‐ 14x + 49
b2
‐142
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( )2 = 25
x2 + 10x = ‐ 13
x2 + 10x + 25 = ‐13 + 25
(x + 5)2 = 12
x + 5 = ±√12
x = ‐5 ± 2√3
Review #2: Solve x2 + 10x + 13 = 0 by completing the square.
Review #3: Now, re‐write the functionin vertex form and find the vertex.
(x + 5)2 = 12
(x + 5)2 ‐ 12 = 0
f(x) = (x + 5)2 ‐ 12
vertex (‐5, ‐12)
10
2
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When the quadratic term has a coefficient that is not 1, you can still solve by completing the square and re‐write the quadratic in vertex form.
Example #1: Solve y = 2x2 ‐ 8x ‐ 15 by completing the square and re‐write the function in vertex form to find the vertex.
y = 2x2 ‐ 8x ‐ 15 2(x ‐ 2)2 = 23
2x2 ‐ 8x ‐ 15 = 0 2(x ‐ 2)2 ‐ 23 = 0
2x2 ‐ 8x = 15 y = 2(x ‐ 2)2 ‐ 23
2(x2 ‐ 4x) = 15 vertex (2, ‐23)
2(x2 ‐ 4x + 4) = 15 + 8
2(x ‐ 2)2 = 23
(x ‐ 2)2 = 11.5
x ‐ 2 = ±√11.5
x = 2 ±√11.5
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Example #2: Solve y = 3x2 + 15x ‐ 27 by completing the square and re‐write the function in vertex form.
y = 3x2 + 15x ‐ 27
3x2 + 15x ‐ 27 = 0
3x2 + 15x = 27
3(x2 + 5x) = 27
3(x2 + 5x + 6.25) = 27 + 18.75
3(x + 2.5)2 = 45.75
(x + 2.5)2 = 15.25
x + 2.5 = ±√15.25
x = ‐2.5 ±√15.25
52( )
2
(2.5)2 6.25
(x + 2.5)2 = 15.25
(x + 2.5)2 ‐ 15.25 = 0
y = (x + 2.5)2 ‐ 15.25
vertex (‐2.5, ‐15.25)
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Homework:page 285
﴾22 27, 30, 32, 33, 37, 39, 69 71﴿