Summary Junior year math notes

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)