Algebra Cheat Sheet Anchor Chart
Algebra Quiz Prep
Essential Patterns & Strategy Guide
1
Vertical Lines
Rule: A vertical line always has the same x-value.
Example: If the point is (-4, 6), the equation is x = -4.
Shortcut: Use the x-coordinate only!
2
Systems (Elimination)
x + 5y = -10
3x - 5y = 10
4x = 0 → x = 0
- Add if signs are opposites
- Subtract if signs are same
- Plug back in to find the second variable
Final Answer = Ordered Pair (x, y)
3
Factoring Trinomials
ALWAYS: Check for a GCF first!
2y2 + 12y - 54
↓
2(y + 9)(y - 3)
MULTIPLY
to last #
ADD
to middle #
4
Vertex Form
y = a(x - h)2 + k
Vertex: (h, k)
Flip the sign of 'h' when taking it out!
+a: MIN (Opens Up)
-a: MAX (Opens Down)
5
Avg. Rate of Change
The Slope Rule
\( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Find the y-values for the given x-interval, then use the slope formula.
6
Linear Equations
y = mx + b
m = slope Rise / Run
b = y-int Crosses y-axis
Monday Quiz Reminders
Vertical lines use x only. Maximum opens down.
Accuracy
Believe
Algebra Blitz Review Worksheet
Algebra Blitz Review
Practice your patterns before Monday's quiz!
Name:
Date:
Problem 1: Vertical Lines
Rule Checklist
Write the equation of the vertical line that passes through the point (7, -3).
Workspace / Calculations
Answer:
Problem 2: Systems by Elimination
Solve for (x, y)
Solve the system using elimination:
\[ \begin{cases} 2x + 4y = 12 \\ 3x - 4y = 8 \end{cases} \]
Show each step clearly
Ordered Pair Solution:
Problem 3: Factoring Completely
GCF First
Factor the following expression completely:
3x² + 18x + 24
Workspace
Factored Form:
Algebra Blitz Review (Page 2)
MONDAY QUIZ PREP
Problem 4: Vertex Form
Quadratic Features
Consider: y = -2(x - 5)² + 8
A) What is the Vertex?
B) Maximum or Minimum?
Problem 5: Average Rate of Change
Slope Over Interval
Find the average rate of change for f(x) = x² - 4 on the interval [1, 4].
1. Find Coordinates
2. Solve for Slope
Average Rate =
Problem 6: Linear Equations
y = mx + b
Write the equation of the line in slope-intercept form:
Slope (m)
-2
y-intercept (b)
5
Equation:
y =
Algebra Blitz Review Answer Key
Answer Key
Algebra Blitz Review - Teacher Solutions
Problem 1: Vertical Lines
Equation of vertical line through (7, -3).
Answer:
x = 7
Problem 2: Systems by Elimination
1. Add: (2x + 3x) + (4y - 4y) = 12 + 8
5x = 20 → x = 4
2. Solve for y: 2(4) + 4y = 12
8 + 4y = 12 → 4y = 4 → y = 1
Ordered Pair:
(4, 1)
Problem 3: Factoring Completely
1. GCF: 3(x² + 6x + 8)
2. Trinomial: Numbers that mult to 8, add to 6 are 4 & 2.
Final Form:
3(x + 4)(x + 2)
Answer Key (Page 2)
TEACHER RESOURCE
Problem 4: Vertex Form
A) Vertex:
(5, 8)
B) Max/Min:
Maximum
Problem 5: Average Rate of Change
f(4) = 4² - 4 = 12
f(1) = 1² - 4 = -3
Rate = (12 - (-3)) / (4 - 1) = 15 / 3 = 5
Average Rate:
5
Problem 6: Linear Equations
m = -2, b = 5
y = -2x + 5
