University:
Henry Ford College
Course:
MATH-115 | College Algebra
Academic year:

2024
Views:

253

Pages:

3
Author:

Hiba N.

📘 Algebra 2 Notes Chapter 1: Linear Equations & Inequalities ● A linear equation looks like: y = mx + b → m = slope, b = y-intercept ● Standard form: Ax + By = C → Try to get it into slope-intercept form to graph it! Solving Linear Equations: 1. Combine like terms 2. Move variables to one side ✔️ 3. Isolate the variable Example: 3x - 5 = 10 → x = 5 Inequalities: ● Similar to equations, but watch the signs!! ✔️ ● If you multiply/divide by a negative → FLIP the inequality Example: -2x > 4 → x < -2 ✏️ Chapter 2: Systems of Equations Ways to solve: 1. Substitution 2. Elimination 3. Graphing (not always super accurate) ✔️ Example: x+y=6 x-y=2 → Add both: 2x = 8 → x = 4 → plug back in: y = 2 Chapter 3: Quadratic Functions Standard form: y = ax² + bx + c Vertex form: y = a(x - h)² + k Vertex = (h, k) ✔️ Ways to solve quadratics: ● Factoring (if easy) ● Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a ● Completing the square ● Graphing (parabola shape!) Chapter 4: Polynomials ✔️ ● Polynomial = expression with multiple terms Example: 3x² + 2x - 5 ✏️ Operations: ● Add/subtract → combine like terms ● Multiply → use distributive or box method ● Divide → long division or synthetic division (kind of annoying but doable) Degree = highest power of x → Helps know how many roots (solutions) it has Chapter 5: Exponents & Radicals Laws of Exponents: ● x^a * x^b = x^(a + b) ● (x^a)^b = x^(a*b) ● x^0 = 1 ● x^-a = 1/x^a Simplifying radicals: ✔️ ● √(a * b) = √a * √b Example: √50 = √(25*2) = 5√2 Chapter 6: Rational Expressions Just fractions with variables! Steps: 1. Factor everything 2. Cancel common factors 3. Watch domain restrictions (can't divide by 0) ✔️ Example: (x² - 4)/(x² - x - 6) = [(x-2)(x+2)] / [(x-3)(x+2)] → Cancel (x+2), left with (x-2)/(x-3)

Linear Equations and Inequalities

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