Final Review Day 2 Algebra 1

Factoring – GCF Method Example: Factor 25 𝑥 4 −5 𝑥 7 +10𝑥 1. Determine the largest # and variable that can be divided into ALL terms (GCF) Example: 5𝑥 2. Divide all terms by the GCF and write the remainder. When dividing variables, SUBTRACT the exponents. Example: 5 𝑥 3 − 𝑥 6 +2 3. Write out the GCF in front of your answer from Step 2. Example: 5𝑥 5 𝑥 3 − 𝑥 6 +2

Factoring – ABC “X” Method 1. Verify it’s simplified/quadratic 𝑎 𝑥 2 +𝑏𝑥+𝑐 2. Fill in the “X” Top: 𝐴∙𝐶 Bottom: 𝐵 Multiplies to top & adds to bottom 3. Rewrite into factors of (ax+___)(ax+___) 4. Simplify any factors

Factoring – Multiple Factoring Methods First, do GCF method. Then, if there’s a simplified quadratic left, use ABC method.

Factor & Solving First, get the equation equal to zero. Then, factor You may need to multiply, then combine like terms first. Then, factor Use GCF, ABC or both Finally, use ZPP

Perfect Square Trinomial Example: 16 𝑥 2 +24𝑥+9= 4𝑥+3 2 You can write the factored form into the same factor squared. Thus, when you do the ABC “X” Method, you should result in the two side numbers being the exact same.

Quadratic Function: Standard Form Example: 𝑦=2 𝑥 2 +9𝑥+4 Vertex (Max or Min of the graph) 𝑥=− 𝑏 2𝑎 , 𝑦= plug in 𝑥 value into equation. Axis of Symmetry (vert. line that cuts graph) 𝑥=− 𝑏 2𝑎 Domain (All possible x values) All Real Numbers Range (All possible y values) 𝑦≥ the minimum value or 𝑦≤ the maximum value

Quadratic Function: Standard Form Example: 𝑦=2 𝑥 2 +9𝑥+4 Zeroes, Roots, X-Intercepts, Solutions Where the graph crosses the x-axis A quadratic function could have one, two, or no solutions

Quadratic Function: Translations Standard/Vertex Vertex Form: 𝑦=𝑎 𝑥−ℎ 2 +𝑘 𝑎: dilations & reflections ℎ: horizontal shifts (left/right) “opposite” 𝑘: vertical shifts (up/down) “as you see it” Standard Form: 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 𝑐: vertical shifts (up/down) “as you see it”

Quiz Scores You can work in a group of maximum 4. Option 1: No Notes 2 points extra credit 2 yes or no questions 1 hint Option 2: Notes Allowed 1 yes or no question