Handoff Sheet: Graphing Quadratics
Session 13 - 7.1 Graphing Quadratics | Week 4
Prepared by: [Instructor Name] | Date: Session 13 (Tuesday, Week 4) | Format: Zoom-based | Duration: 2 hours
Session Snapshot
Session at a Glance
| Element |
Details |
| Outcome |
Outcome 6: Graph quadratic functions by identifying vertex, intercepts, and additional points. |
| Session Code |
7.1 - Graphing Quadratics |
| Week & Day |
Week 4, Tuesday |
| Class Structure |
1:30-2:00 PM (Socratic, 30 min) + 2:00-3:00 PM (Workshop, 60 min) + 3:00-3:30 PM (Independent, 30 min) |
| Learning Mode |
Zoom-based (main room Socratic; breakout rooms for workshop) |
| Key Topic |
Graphing parabolas: vertex (x = −b/(2a)), y-intercept, symmetry, sketching |
| Builds On |
Session 12 (Intro to Quadratics: formulas, domain/range, transformations) |
| Leads To |
Session 14 (Solving Quadratic Equations: quadratic formula, x-intercepts) |
Materials Checklist
Provided Files (6 total)
All files in session folder:
- ☐ Reading - Graphing Quadratics.html (Student reading, pre-class)
- ☐ Socratic Guide - Graphing Quadratics.html (Instructor facilitation, 30 min)
- ☐ Worksheet - Graphing Quadratics.html (Student deliverable, 35 pts)
- ☐ Session Notes - Graphing Quadratics.html (Detailed session plan)
- ☐ Answer Key - Graphing Quadratics.html (Grading reference)
- ☐ Handoff Sheet - Graphing Quadratics.html (This file)
External Resources
- nwic-style.css (shared stylesheet, linked in all HTML files)
- Desmos Graphing Calculator (free, online; open during session for live verification)
- YouTube Videos (embedded in Reading; also optional for students)
- Graph Paper (for student sketches; can be digital or printed)
Content Map
Reading: Three-Lane Approach
- Story Lane: Basketball arc narrative; why graphing matters
- Visual Lane: Parabola shape, key points table, transformations, YouTube videos
- Traditional Lane: Step-by-step algorithm (5 steps to graph), formulas, examples, real-world applications
Core Concepts
- Vertex Formula: x = −b/(2a); plug back to find y
- Y-Intercept: Set x = 0; y = c
- X-Intercepts (Preview): Set y = 0; factor or quadratic formula (Session 14)
- Symmetry: Parabolas symmetric about vertical line through vertex
- Coefficient a Effects: Sign determines direction; magnitude determines width
- Real-World Applications: Basketball arc, revenue curve, bridge arch
Key Examples in Session
- y = x² − 4x + 3 (vertex, y-int, x-ints, sketch)
- y = −x² + 6x − 5 (downward parabola)
- y = x² − 2x − 3 (upward parabola)
- h(x) = −0.1x² + 0.8x + 6 (basketball arc)
- P(p) = −2p² + 40p − 150 (revenue optimization)
Pacing Guide
Session Timeline (120 min total)
| Time |
Activity |
Duration |
Instructor Lead / Student Driven |
| 1:30-1:35 |
Opening hook (basketball video) |
5 min |
Instructor lead |
| 1:35-1:43 |
Vertex discovery (y = x² − 4x + 3) |
8 min |
Socratic (instructor poses, students think) |
| 1:43-1:51 |
Y-intercept & symmetry |
8 min |
Socratic with calculation |
| 1:51-1:58 |
X-intercepts (preview) & complete picture |
7 min |
Guided, minimal student calculation |
| 1:58-2:00 |
Transition to workshop |
2 min |
Instructor summary |
| WORKSHOP SEGMENT (2:00-3:00 PM) |
60 min |
|
| 2:00-2:15 |
Guided practice (y = 2x² − 12x + 10) |
15 min |
Instructor models all steps |
| 2:15-2:35 |
Pair work (y = −x² + 6x − 5) |
20 min |
Student-driven; instructor circulates |
| 2:35-2:45 |
Desmos verification & live feedback |
10 min |
Instructor demo & student exploration |
| 2:45-3:00 |
Real-world applications (bridge arch, revenue) |
15 min |
Instructor leads; students contribute |
| INDEPENDENT SEGMENT (3:00-3:30 PM) |
30 min |
|
| 3:00-3:30 |
Students work on Worksheet; instructor circulates |
30 min |
Student-independent; instructor support as needed |
Facilitation Notes
Socratic Discussion Strategy
- Ask, don't tell. “What shape is the arc?” rather than “It’s a parabola.”
- Embrace productive struggle. Let silence hang for 5-10 seconds after a question.
- Listen for misconceptions. “Does the vertex have to be on the x-axis?” signals confusion.
- Use follow-up prompts. “Can you say more about that?” or “How do you know?”
- Highlight big ideas. After a student answer, rephrase to reinforce: “So the vertex is the turning point, and the formula x = −b/(2a) always finds it.”
Workshop Breakout Management
- Assign students to pairs thoughtfully (strong + developing, if possible)
- Set clear time markers: “You have 10 minutes; then we regroup.”
- Circulate to each breakout room at least twice
- Ask probing questions: “What did you get for the vertex? How did you find it?”
- Provide immediate corrective feedback if vertex calculation is wrong
- Celebrate effort: “I like how you used symmetry to check your work.”
Desmos Integration
- Open Desmos before the session starts
- During workshop, type in one function live (e.g., y = x² − 4x + 3)
- Point out the vertex, y-intercept, x-intercepts on the graph
- Ask: “Does your sketch match this?”
- Encourage students to open Desmos themselves and explore
- Use it to debunk misconceptions: “See? The parabola does cross the x-axis at (1, 0) and (3, 0).”
Common Misconceptions & Responses
Misconception 1: “The vertex must be on the x-axis.”
Response: “Not necessarily. The vertex is the turning point. It can be above the x-axis, below it, or touching it. Let’s check (2, −1) for y = x² − 4x + 3. Is it on the x-axis? No, it’s below it, at y = −1. That’s fine.”
Misconception 2: “The x-intercepts are the same as the vertex.”
Response: “Different points. The vertex is the turning point. The x-intercepts are where the graph crosses the x-axis. For y = x² − 4x + 3, the vertex is (2, −1), but the x-intercepts are (1, 0) and (3, 0). The vertex is between the x-intercepts.”
Misconception 3: “Parabolas must be symmetric top-to-bottom.”
Response: “Parabolas are symmetric left-to-right, about the vertical line through the vertex. That’s the axis of symmetry. For y = x² − 4x + 3, the axis is x = 2. Points equidistant from x = 2 have the same y-value.”
Assessment Strategy
Worksheet Grading (35 pts)
- Part A (15 pts): Graph y = −x² + 6x − 5
- Part B (10 pts): Graph y = x² − 2x − 3
- Part C (5 pts): Coefficient a explanation
- Part D (5 pts): Real-world application
Resubmission Threshold
- If score < 25/35: Student may revise and resubmit within 5 days
- Focus feedback on: vertex calculation, y-intercept, symmetry concept, sketch quality
- Encourage use of Desmos to verify
Technology Requirements
Tech Setup
| Tool/Platform |
Use |
Required / Optional |
| Zoom |
Main class meeting; Socratic discussion; breakout rooms for workshop |
Required |
| Desmos (free online) |
Live graphing during workshop; student verification |
Required |
| HTML Files (Reading, Socratic Guide, Worksheet, etc.) |
Instruction, reference, deliverable |
Required |
| Graph Paper / Digital Drawing |
Student sketching for worksheet |
Required |
| GeoGebra (optional) |
Alternative to Desmos for verification |
Optional |
| Zoom Whiteboard / OneNote |
Annotation and live work during Socratic |
Optional but helpful |
Student Preparation
Pre-Session (Asynchronous)
- Read: Reading - Graphing Quadratics (all three lanes)
- Watch embedded YouTube videos (Khan Academy)
- Review formulas: x = −b/(2a), y = c, symmetry concept
- Have graph paper or digital drawing tool ready
During Session
- Socratic (1:30-2:00 PM): Listen, take notes, respond to questions
- Workshop (2:00-3:00 PM): Work with partner, practice graphing, use Desmos to verify
- Independent (3:00-3:30 PM): Begin Worksheet; complete at home if needed
Post-Session (Asynchronous)
- Complete Worksheet (Parts A-D, 35 pts total)
- Submit by [DATE] to assignment portal
- If score < 25/35, revise and resubmit within 5 days
Instructor Prep Checklist
1 Week Before Session:
- ☐ Review all 6 HTML files (Reading, Socratic Guide, Worksheet, Session Notes, Answer Key, Handoff Sheet)
- ☐ Double-check nwic-style.css is linked and renders correctly
- ☐ Test Desmos online graphing tool in your browser
- ☐ Print or PDF Worksheet for reference during grading
- ☐ Generate 3-4 additional quadratic functions for contingency practice problems
1 Day Before Session:
- ☐ Test Zoom setup: audio, video, screen share, breakout rooms
- ☐ Prepare Zoom whiteboard or OneNote annotation tool
- ☐ Open Desmos in a browser tab (have it ready to share)
- ☐ Review Socratic Guide; highlight key transition points
- ☐ Write out vertex calculations for y = x² − 4x + 3 on a notecard (reference)
- ☐ Send pre-session reminder to students: Read the material, have graph paper ready
15 Minutes Before Session:
- ☐ Join Zoom call early; test screen share
- ☐ Load Desmos in a second browser window
- ☐ Open Socratic Guide in a tab for reference
- ☐ Have Session Notes open for pacing
- ☐ Ensure recording is ON (if recording for archival)
- ☐ Greet students as they join; welcome them by name
After Session:
- ☐ Download Zoom recording (if applicable)
- ☐ Send debrief message: “Great session! Here’s your Worksheet link. Due [DATE].”
- ☐ Grade first 2-3 worksheets to catch patterns early
- ☐ Provide feedback within 48 hours; flag resubmissions
- ☐ Note any misconceptions or topics to revisit in Session 14
Transition to Session 14
Session 14 Focus: Solving Quadratic Equations (7.2)
- What students will do: Use the quadratic formula to find x-intercepts precisely; solve ax² + bx + c = 0
- How it builds on Session 13: Students now know what x-intercepts look like on a graph (Session 13). Session 14 teaches how to calculate them algebraically.
- Real-world extension: Session 14 answers “When does the ball land?” and “At what price does profit = 0?”
- Quick recall: In Session 14, be ready to reference Session 13 graphs and ask, “Where are the x-intercepts on this parabola? Let’s find them algebraically.”
Recommended Reading Order for Handoff
Handoff to another instructor? Read in this order:
- This Handoff Sheet (overview)
- Session Notes (detailed session plan)
- Socratic Guide (exact questions to pose)
- Worksheet (what students will submit)
- Answer Key (how to grade)
- Reading (student reference; skim to familiarize)
Contact & Support
Questions about this session?
- Review the Session Notes for detailed facilitation guidance
- Check the Socratic Guide for exact questioning strategies
- Reference the Answer Key if uncertain how to grade a student response
- Reach out to the curriculum coordinator: [Email/Phone]
Session 13 is ready to teach. Good luck!