Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 9 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 6 — Analyze quadratic functions by identifying vertex, axis of symmetry, intercepts, and maximum/minimum values, and graph parabolas in both standard and vertex form.

This file holds two pieces: (A) the Module 9 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 9 meeting Tue Oct 27 and Thu Oct 29, and end-of-week work due Sunday Nov 1, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 9 Overview — Start Here

Welcome to Week 9: Quadratic Functions & Their Graphs

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Welcome back from the midterm. You've cleared the first big checkpoint — real numbers, linear functions, systems, polynomials, and quadratic equations are all behind you. Week 9 opens the second half with one of the most important shapes in mathematics: the parabola. Two weeks ago (Week 7) you learned to solve quadratic equations. This week you learn to see them — to look at a quadratic function and immediately read off its vertex, its axis of symmetry, its direction, and its highest or lowest value. The algebraic skills from the first half of the course make this week feel like payoff.

The week's big question

"Given a quadratic function, what can I read off its graph — and how do I find each feature from the formula?"

By Sunday you'll be able to find the vertex from either form of a quadratic, sketch the parabola from its key features, identify the axis of symmetry, locate all intercepts, and decide whether the function has a minimum or maximum — and why.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Identify the vertex and axis of symmetry — from vertex form f(x) = a(x − h)² + k (vertex is (h, k)) and from standard form f(x) = ax² + bx + c (x = −b/(2a)).
• [ ] Find all intercepts — y-intercept by evaluating f(0) = c; x-intercepts by solving ax² + bx + c = 0 (or reading the discriminant).
• [ ] Determine direction and min/max — a > 0 means the parabola opens up and has a minimum at the vertex; a < 0 means it opens down and has a maximum.
• [ ] Apply quadratic functions to real-world problems — set up a projectile-motion or optimization model, find the vertex, and interpret the result in context.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work. Chatbots sometimes misread the sign of h in vertex form — (x − 2)² + 3 has vertex (2, 3), not (−2, 3) — and they occasionally confuse minimum and maximum. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Vertex form is the shortcut. Once you can eyeball h and k from f(x) = a(x − h)² + k, everything else falls into place: axis = x = h, direction from a, max/min value = k.
• Memorize the two sign traps. In (x − h)², the vertex x-coordinate is h, not −h — the formula already has the subtraction built in. And −b/(2a) for standard form requires the negative sign — don't compute b/(2a).
• Let Desmos confirm your sketch. Type the function, check that the vertex and intercepts land where you expect. If they don't, find the algebra error before the quiz does.
• For applications: vertex = answer. In every max/min word problem, the answer lives at the vertex. Set up the quadratic, find the vertex with x = −b/(2a), plug back in, and interpret in plain language.
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. That habit is the whole semester in miniature.

You're starting the second half fresh. See you Tuesday.

(B) Welcome Announcement — Module 9

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Oct 26, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Oct 26."

Subject: Week 9 is here — welcome back, now let's see that parabola 👋

Hi everyone,

Welcome back from the midterm. You've cleared a big milestone — everything from real numbers through quadratic equations is behind you, and I hope the exam showed you how much you've actually learned. Now we open Week 9 and the second half of the course, and we do it with one of my favorite topics: quadratic functions and their graphs.

This week's big question: Given a quadratic function, what can I read off its graph — and how do I find each feature from the formula? By Sunday you'll be reading vertices, axes of symmetry, intercepts, and maximum/minimum values straight from the equation — in both vertex form and standard form — and applying that to real-world problems involving projectile paths and optimization.

Three things not to miss:
1. Lecture Tutorial 9 — work through vertex form, standard form, intercepts, direction, and min/max with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. Catch any sign errors the model makes. Due Sun Nov 1.
2. Quiz 9 (no AI on quizzes) and Discussion 9 — "Parabolas in Your World" also close Sun Nov 1 — the discussion asks where max/min problems show up in your own field or life, so start early and leave time to reply to classmates.
3. Assignment 9 — four AI-coached problems with a self-scored report; due Sun Nov 1.

One promise: everything you practice this week — finding vertices, reading intercepts, interpreting min/max — feeds directly into the polynomial and rational function work coming in Weeks 10–12. Build the habit of sketching the graph first; it pays off all the way to the final.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring a pencil and a graphing tool (Desmos works great for this week). See you Tuesday.

See you soon,
Prof. Calloway