Function Tracker Worksheet
Parabola Plotter
Lab Report: Stage 01
Pilot Name
Launch Date
MISSION PROTOCOL: Choose 5 integers for x (centered at 0). Calculate y. Plot and connect with a smooth, symmetrical curve.
01
y = x2 - 4
| Input (x) | Calculation (Work Space) | Output (y) |
|---|
| -2 | | |
| -1 | | |
| 0 | | |
| 1 | | |
| 2 | | |
X Y
Parabola Plotter
Lab Report: Stage 02
02
y = -x2 + 2
| Input (x) | Calculation (Work Space) | Output (y) |
|---|
| -2 | | |
| -1 | | |
| 0 | | |
| 1 | | |
| 2 | | |
X Y
Parabola Plotter
Lab Report: Final Analysis
03
y = 2x2 - 6
Mission Debrief
1. Pattern Recognition: Compare #01 and #02. What happens to the direction of the "U" shape when the x2 term is negative?
2. Constant Value: Look at the number without a variable. Where do you see this number appear on your graph's vertical axis?
Parabola Plotting Slides
Parabola Plotting
Navigating Quadratic Functions
The Curve
STAGE 01
A Quadratic Function creates a U-shaped curve called a Parabola.
- Perfectly symmetrical.
- Has a Vertex (Min/Max).
Vertex
The Blueprint
STAGE 02
y = ax2 + c
Variable a
Controls direction. Positive opens UP; Negative opens DOWN.
Variable c
Controls height. It shifts the vertex vertically and is the y-intercept.
Spreadsheet Strategy
STAGE 03
The Table Method
Organize your data like a data entry professional.
Expert Tip:
Start with x = 0. For these simple forms, the vertex is always the y-intercept!
| x | Work | y |
|---|
| -1 | (-1)² - 4 | -3 |
| 0 | (0)² - 4 | -4 |
| 1 | (1)² - 4 | -3 |
Launch Sequence
STAGE 04
1
Input
Choose integers around zero.
2
Process
Solve for y for every input row.
3
Map
Plot pairs on the grid system.
4
Trace
Connect with a smooth curve.
Tracker Key Teacher Guide
Answer Key Master
Topic 4.1: Quadratic Graphing Fundamentals
TEACHER REFERENCE
Solution Spreadsheet
| Function Equation | Vertex | Opening | y-values (x = -2 to 2) |
|---|
| Problem 1: y = x2 - 4 | (0, -4) | UP (MIN) | 0, -3, -4, -3, 0 |
| Problem 2: y = -x2 + 2 | (0, 2) | DOWN (MAX) | -2, 1, 2, 1, -2 |
| Problem 3: y = 2x2 - 6 | (0, -6) | UP (MIN) | 2, -4, -6, -4, 2 |
Analysis Solutions
Q1: Negative Term Effect
"The parabola opens downward instead of upward."
Q2: Constant Value
"The constant is the y-intercept (and vertex in these forms)."
Audit Checklist
- Symmetry across the y-axis.
- Vertex is correctly identified as a min/max.
- Problem 3 is narrower than Problem 1.
Instructional Support
Squaring Negatives
Stress that squaring a negative number like (-2)2 always results in a positive (4). Remind students to use parentheses on calculators.
Smooth Curves
Monitor students to ensure they are not drawing "V" shapes. Parabolas are smooth, continuous curves that turn at the vertex.
