1. Algebra Review
Laws of Exponents:
• a^m \cdot a^n = a^{m+n}
• \frac{a^m}{a^n} = a^{m-n}
• (a^m)^n = a^{m \cdot n}
• a^{-n} = \frac{1}{a^n}
• (ab)^n = a^n \cdot b^n
• \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
Factoring Tricks:
• Difference of Squares: a^2 - b^2 = (a - b)(a + b)
• Perfect Square Trinomials:
• a^2 + 2ab + b^2 = (a + b)^2
• a^2 - 2ab + b^2 = (a - b)^2
• Quadratic Formula:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
2. Functions & Graphing
Types of Functions:
• Linear: f(x) = mx + b (slope = m , y-intercept = b )
• Quadratic: f(x) = ax^2 + bx + c
• Exponential: f(x) = a \cdot b^x
• Logarithmic: f(x) = \log_b(x)
Transformations:
• Vertical Shift: f(x) + k (up if k > 0 , down if k < 0 )
• Horizontal Shift: f(x - h) (right if h > 0 , left if h < 0 )
• Reflections:
• -f(x) (reflect over x-axis)
Laws of Exponents:
• a^m \cdot a^n = a^{m+n}
• \frac{a^m}{a^n} = a^{m-n}
• (a^m)^n = a^{m \cdot n}
• a^{-n} = \frac{1}{a^n}
• (ab)^n = a^n \cdot b^n
• \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
Factoring Tricks:
• Difference of Squares: a^2 - b^2 = (a - b)(a + b)
• Perfect Square Trinomials:
• a^2 + 2ab + b^2 = (a + b)^2
• a^2 - 2ab + b^2 = (a - b)^2
• Quadratic Formula:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
2. Functions & Graphing
Types of Functions:
• Linear: f(x) = mx + b (slope = m , y-intercept = b )
• Quadratic: f(x) = ax^2 + bx + c
• Exponential: f(x) = a \cdot b^x
• Logarithmic: f(x) = \log_b(x)
Transformations:
• Vertical Shift: f(x) + k (up if k > 0 , down if k < 0 )
• Horizontal Shift: f(x - h) (right if h > 0 , left if h < 0 )
• Reflections:
• -f(x) (reflect over x-axis)
