Graph Guru Worksheet
Graph Guru
Quadratic Features Analysis
Name:
Date:
Technical Specifications
Analyze each quadratic function below. Identify and label the following key features on the graph: Vertex, Axis of Symmetry (AoS), x-intercepts, and y-intercept. Then, identify if the function has a Minimum or Maximum value.
01 f(x) = x² - 4
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
02 f(x) = -(x - 2)² + 1
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
03 f(x) = x² - 2x - 3
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
04 f(x) = -x² + 4x
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
Phase 2: Complex Forms
BACK PAGE
05 f(x) = (x + 1)² - 4
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
06 f(x) = x² + 6x + 9
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
07 f(x) = -2x² + 8
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
08 f(x) = x² - 4x + 3
Vertex:
AoS:
x-intercepts:
y-intercept:
Value Type:
Min
Max
Architect's Summary
How does the sign of the leading coefficient (a) determine if a function has a minimum or maximum value?
Root Rewriter Worksheet
Root Rewriter
From Solutions to Factors
Name:
Date:
Factory Assembly
For the given roots or equations, determine the linear factors and write the quadratic in factored form. If a root is a fraction \( a/b \), use the integer coefficient factor \( (bx - a) \).
1
Roots:
x = 4, -2
Factors:
Factored Form f(x) =
2
Roots:
x = 0, 7
Factors:
Factored Form f(x) =
3
Equation:
x² + 10x + 25 = 0
Roots
Factors
Factored Form f(x) =
4
Equation:
2x² - 7x + 3 = 0
Roots
Factors
Factored Form f(x) =
Phase 2: Rational Challenges
BACK PAGE
5
Roots:
x = -3/4, 2/3
Factors:
Factored Form f(x) =
6
Roots:
x = 10, -10
Factors:
Factored Form f(x) =
7
Equation:
5x² + 19x - 4 = 0
Roots
Factors
Factored Form f(x) =
8
Equation:
2x² + x - 3 = 0
Roots
Factors
Factored Form f(x) =
The Vocabulary Vault
List three other mathematical terms that mean the same as roots:
Graph Guru Answer Key
Answer Key
Graph Guru Worksheet
Teacher Resource
01 f(x) = x² - 4
Vertex: (0, -4)
AoS: x = 0
x-intercepts: (-2, 0), (2, 0)
y-intercept: (0, -4)
Type: Minimum
02 f(x) = -(x - 2)² + 1
Vertex: (2, 1)
AoS: x = 2
x-intercepts: (1, 0), (3, 0)
y-intercept: (0, -3)
Type: Maximum
03 f(x) = x² - 2x - 3
Vertex: (1, -4)
AoS: x = 1
x-intercepts: (-1, 0), (3, 0)
y-intercept: (0, -3)
Type: Minimum
04 f(x) = -x² + 4x
Vertex: (2, 4)
AoS: x = 2
x-intercepts: (0, 0), (4, 0)
y-intercept: (0, 0)
Type: Maximum
05 f(x) = (x + 1)² - 4
Vertex: (-1, -4)
AoS: x = -1
x-intercepts: (-3, 0), (1, 0)
y-intercept: (0, -3)
Type: Minimum
06 f(x) = x² + 6x + 9
Vertex: (-3, 0)
AoS: x = -3
x-intercepts: (-3, 0)
y-intercept: (0, 9)
Type: Minimum
07 f(x) = -2x² + 8
Vertex: (0, 8)
AoS: x = 0
x-intercepts: (-2, 0), (2, 0)
y-intercept: (0, 8)
Type: Maximum
08 f(x) = x² - 4x + 3
Vertex: (2, -1)
AoS: x = 2
x-intercepts: (1, 0), (3, 0)
y-intercept: (0, 3)
Type: Minimum
Quadratic Quests Slides
Quadratic Quests
Decoding the Parabola
Parabola Anatomy
V
Vertex
The highest (max) or lowest (min) point on the graph.
A
Axis of Symmetry
The vertical line that cuts the parabola into two mirror images.
I
Intercepts
Where the graph crosses the X and Y axes.
The Root-to-Factor Rule
If a quadratic has a root (solution) at x = r, then its linear factor is:
(x - r)
Positive Root
Root: x = 5
Factor: (x - 5)
Negative Root
Root: x = -3
Factor: (x + 3)
Rational Roots: The "Bottom-Up" Rule
If your root is:
x = a / b
Your factor is:
(bx - a)
Example: Root 2/3 becomes (3x - 2)
