1. Final Review Day 3
Algebra 1

2. Completing the Square Example: Complete the square of 𝑥 2 −4𝑥+8
Step 1: Find 𝑐= 𝑏 2 2
Step 2: Put your blanks in and fill 𝑐 in with the number
Step 3: Factor into 𝑥± 𝑏 2 2

3. Completing the Square: Writing into Vertex Form
Write into vertex form: 𝑦= 𝑥 2 −4𝑥+8
Step 1: Find 𝑐= 𝑏 2 2
Step 2: Put your blanks in and fill 𝑐 in with the number
Step 3: Factor into 𝑥± 𝑏 2 2
Step 4: Get 𝑦 alone

4. Simplify Radicals Example: 56 𝑥 7 𝑦 2 𝑧 Create a factor tree
Pull out the pairs
Write one of the pairs as a coefficient (outside)
Write the remainders as radicands (inside/leftovers)

5. Multiply/Divide Radicals
Example: 5 3 ∙2 7
Multiply the coefficients and multiple the radicands separately
Simplify using the factor tree if necessary

6. Quadratic Formula
If the ABC “X” Method fails, use the quadratic formula
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

7. Discriminant The discriminant is 𝑏 2 −4𝑎𝑐
It helps determine how many solutions there are without actually fully solving
If 𝑏 2 −4𝑎𝑐<0, there are no real solutions
If 𝑏 2 −4𝑎𝑐>0, there are 2 solutions
If 𝑏 2 −4𝑎𝑐=0, there is one solution

8. Modeling Data Example: Determine the function the table models
1. First Differences: Linear
2. Second Differences: Quadratic
3. Multiply/Divide Same #: Exponential
4. Alternatively, plot the points and determine the function from the shape of the graph.

9. Radical Function Transformations
Given 𝑦=𝑎 𝑥−ℎ +𝑘
𝑎: Reflections & Dilations
ℎ: Horizontal Shifts (left/right: opposite)
𝑘: Vertical Shifts (up/down: as you see it)

10. Radical Functions: Domain/Range
Given 𝑦=𝑎 𝑥−ℎ +𝑘
Domain: 𝑥≥ℎ or 𝑥≤ℎ (depends on the graph)
Range: 𝑦≥𝑘 or 𝑦≤𝑘 (depends on the graph)

11. 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