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2. ALGEBRA ~COMPLETING THE SQUARE: EG: (x + 1)² = x² + x + x + 1 EG: solve for x: + (x + 5)² = 24 x + 5 =√√24 x = 5 ± √√√24 x² + 10x + 1 = 0 1x² + 10x + (5)² = -1 + (5) ² (x-4)² = 14 x-4 = ²√14 EG: 2x²-16x + 4 = 0 x² - 8x =-2 x² = 8x + (4)² = −2+ (4) ² 11₁x0=4=√17² ~MINIMUM ↓ = x² + 2x + 1 EG: (1)² = 1 y = + (x - 1)² + 10 y=+(x-1)²-10 EG: Write y=x²-10x + 3 in the form: y = a (x+p)² +q₂_ y = (x² - 10x + 5² ) -5² +3 y=1(x-5)² -22 a(x+p)² + q Min because besore () is + (3 coefficent of xc)² = last number ~MAXIMUM y==(x-1)² + 10 y = -(x-1)² -10 1 max because before () is -
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Stefan S, iOS User
SuSSan, iOS User
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solving equations
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These notes cover the basics of Pre-Algebra and provides a brief glimpse of Pre-Algebra. Topics: Two-Step Equations, Combine Like Terms, Distributing, Multi-Step Equations, Equations With Variables on Both Sides, and Variable Expressions.
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Solving absolute value equations
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graphing and solving inequalities
2. ALGEBRA ~COMPLETING THE SQUARE: EG: (x + 1)² = x² + x + x + 1 EG: solve for x: + (x + 5)² = 24 x + 5 =√√24 x = 5 ± √√√24 x² + 10x + 1 = 0 1x² + 10x + (5)² = -1 + (5) ² (x-4)² = 14 x-4 = ²√14 EG: 2x²-16x + 4 = 0 x² - 8x =-2 x² = 8x + (4)² = −2+ (4) ² 11₁x0=4=√17² ~MINIMUM ↓ = x² + 2x + 1 EG: (1)² = 1 y = + (x - 1)² + 10 y=+(x-1)²-10 EG: Write y=x²-10x + 3 in the form: y = a (x+p)² +q₂_ y = (x² - 10x + 5² ) -5² +3 y=1(x-5)² -22 a(x+p)² + q Min because besore () is + (3 coefficent of xc)² = last number ~MAXIMUM y==(x-1)² + 10 y = -(x-1)² -10 1 max because before () is -
2. ALGEBRA ~COMPLETING THE SQUARE: EG: (x + 1)² = x² + x + x + 1 EG: solve for x: + (x + 5)² = 24 x + 5 =√√24 x = 5 ± √√√24 x² + 10x + 1 = 0 1x² + 10x + (5)² = -1 + (5) ² (x-4)² = 14 x-4 = ²√14 EG: 2x²-16x + 4 = 0 x² - 8x =-2 x² = 8x + (4)² = −2+ (4) ² 11₁x0=4=√17² ~MINIMUM ↓ = x² + 2x + 1 EG: (1)² = 1 y = + (x - 1)² + 10 y=+(x-1)²-10 EG: Write y=x²-10x + 3 in the form: y = a (x+p)² +q₂_ y = (x² - 10x + 5² ) -5² +3 y=1(x-5)² -22 a(x+p)² + q Min because besore () is + (3 coefficent of xc)² = last number ~MAXIMUM y==(x-1)² + 10 y = -(x-1)² -10 1 max because before () is -
iOS User
Stefan S, iOS User
SuSSan, iOS User