# College Algebra

## Factoring Polynomials

OpenStax. Ch. 1 Introduction to Prerequisites - College Algebra. Vertex form introduction. Completing the Square: Finding the Vertex. Completing the Square: Finding the Vertex (page 1 of 2) The vertex form of a quadratic is given by y = a(x – h)2 + k, where (h, k) is the vertex.

The "a" in the vertex form is the same "a" as in y = ax2 + bx + c (that is, both a's have exactly the same value). The sign on "a" tells you whether the quadratic opens up or opens down. Think of it this way: A positive "a" draws a smiley, and a negative "a" draws a frowny. (Yes, it's a silly picture to have in your head, but it makes is very easy to remember how the leading coefficient works.)

In the vertex form of the quadratic, the fact that (h, k) is the vertex makes sense if you think about it for a minute, and it's because the quantity "x – h" is squared, so its value is always zero or greater; being squared, it can never be negative. Suppose that "a" is positive, so a(x – h)2 is zero or positive and, whatever x-value you choose, you're always taking k and adding a(x – h)2 to it. Find the vertex of y = 3x2 + 2x – 1. College algebra supplementary information. Absolute Value Abolute Value Inequalities All about ALEKS Applications Average Rate of Change Function Binomial Theorem Calculator Tips Common Algebra Errors Completing the square Conics (Parabola, Ellipse, Hyperbola) Conics - Building Equations Determinant - combining row operations with expanding by cofactors Domain Dot-Cross Technique Even & Odd Functions Function Notation Gaussian Elimination Method to Solve Systems of Linear Equations Greatest Common Factor Partial Fraction Decomposition Pencasts of Sample Problems Point on a curve closest to a fixed point Proof by Math Induction Polynomials and their Zeros Polynomials - LUB and GLB for the real roots Rational Functions Review for the Final Exam Sequences - Proofs of Arithmetic & Geometric Sequences & Series - General terms A Study of Symmetry Systems of Linear Equations - infinite solutions Cool video - math behind the 9-11 memorial Vocabulary.

## Common Graphs

MATH 1314: College Algebra. Copyright This courseware includes resources copyrighted and openly licensed by multiple individuals and organizations.

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