Advanced Algebraic Concepts and Graphing
This page delves deeper into algebraic concepts, focusing on graphing linear inequalities, exponential functions, and more advanced topics in algebra.
The section on graphing linear inequalities explains how to use the y = mx + b form to graph inequalities. It provides an example and important notes:
Example: To graph x - y ≤ 4, rearrange it to y ≥ -4 + x.
Highlight: When multiplying or dividing an inequality by a negative number, the inequality sign flips.
The page introduces exponential functions in the form y = a·bˣ, explaining that if b > 1, the function will increase. It also covers exponential growth and geometric sequences.
Definition: Exponential growth is represented by the formula y = a(1+r)ᵗ, where a is the initial amount, r is the rate, and t is time.
The arithmetic sequence formula is presented as aₙ = d(n-1) + a, where d is the common difference between terms.
The page then moves on to more advanced topics, including exponent rules, the difference of squares, and FOIL (First, Outer, Inner, Last) method for multiplying binomials.
Example: Using FOIL to multiply (x+2)(x+3) = x² + 5x + 6
Factoring trinomials is explained, including the "slip and slide" method for trinomials with a coefficient on x².
The page concludes with a brief explanation of scientific notation, showing how to convert numbers to and from this format.
Vocabulary: Scientific notation is expressed as A × 10ⁿ, where 1 ≤ |A| < 10 and n is an integer.
This page provides a wealth of information on advanced algebraic concepts, building upon the foundations laid in the previous page.
