Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 7 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 6 — Solve quadratic equations by factoring, the square root property, completing the square, and the quadratic formula; interpret the discriminant.

This file holds two pieces: (A) the Module 7 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates assume a Tuesday/Thursday session pattern with Week 7 meeting Tue Oct 13 and Thu Oct 15, and end-of-week work due Sunday Oct 18, 11:59 p.m. (Module start date: Mon Oct 12. No holiday this week.) Adjust day-of-week and times to match your section.

(A) Module 7 Overview — Start Here

Welcome to Week 7: Quadratic Equations

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.

This week is the course's first big pivot: we leave the straight-line world and step into curves. Every equation we've solved so far has had a degree of 1 — one unknown, one step to isolate it. A quadratic equation has a squared term, which changes everything. Instead of one solution you get (at most) two, and whether those solutions are real or not depends on a single number called the discriminant. Four methods, one question — and by Friday you'll own all of them.

The week's big question

"When a quadratic equation can be solved four different ways, how do you pick the right one — and how do you know in advance how many real solutions to expect?"

By Sunday you'll factor quadratics and apply the zero-product property in your sleep, use the square root property when there's no x-term, complete the square with confidence, and reach for the quadratic formula as your guaranteed fallback. You'll also read the discriminant at a glance and know before you solve whether you'll get two real answers, one repeated answer, or no real answers at all.

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.

• [ ] Factor a quadratic and apply the zero-product property — write the equation as a product of linear factors, set each to zero, solve.
• [ ] Use the square root property — isolate a perfect square, take ±√, solve both cases.
• [ ] Complete the square — manufacture the perfect-square form and then apply the square root property; understand why it always works.
• [ ] Apply the quadratic formula x = (−b ± √(b²−4ac)) / (2a) — identify a, b, c correctly (including signs), simplify cleanly, and interpret the discriminant b²−4ac: positive → two distinct real solutions; zero → one repeated real solution; negative → no real solutions.

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 frequently fumble quadratics — they'll drop the ± sign, misread the sign of b in the formula, or lose a root by dividing both sides by x. 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

• Learn all four methods, not just the formula. The quadratic formula always works, but factoring is faster when the numbers cooperate — and completing the square is what you'll use in W9 to graph parabolas. Every method has a moment.
• The discriminant is your preview screen. Before you solve, compute b²−4ac. If it's negative, stop — no real solutions exist. If it's zero, expect a repeated root. This five-second check prevents wasted work.
• Watch the signs in the quadratic formula. The formula has −b at the top, which means you must negate whatever b is. If b = −4, then −b = +4. Sign errors here account for most of the lost points on this week's quiz.
• Never divide both sides by x. If you have x² + 3x = 0 and you divide by x, you lose the solution x = 0. Factor out x instead: x(x + 3) = 0.
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. That habit is the whole semester in miniature.

Quadratics are the gateway to everything nonlinear in this course — functions, graphs, max/min, modeling. Nail the methods this week and W9 (quadratic functions) will feel natural. See you Tuesday.

(B) Welcome Announcement — Module 7

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Oct 12, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Oct 12."

Subject: Week 7 — the big pivot from lines to curves

Hi everyone,

Quick check-in: if you were asked right now to solve x² − 5x + 6 = 0, would you know what to do? By Sunday you'll have four ways to answer that question — and you'll know which one to reach for first.

This week — Quadratic Equations — we tackle the big question: When four methods all work, how do you choose the right one — and how do you know in advance whether to expect two answers, one, or zero? The answer is a single number called the discriminant, and it gives you a preview of the solution before you ever start solving.

Three things not to miss:
1. Lecture Tutorial 7 — work through all four quadratic methods with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. You'll catch the model's sign errors, not just trust it. Due Sun Oct 18.
2. Quiz 7 (no AI on quizzes) and Discussion 7 — "Which method would YOU choose?" also close Sun Oct 18 — the discussion is a method-choice argument you work out with an AI partner, so start early.
3. Assignment 7 — four AI-coached problems across all four methods; due Sun Oct 18.

One thing to watch: the quadratic formula has −b at the top. That minus sign is not optional. If b = −3, then −b = +3. I will make sure this trap appears on the quiz, and so should you before you take it.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. See you Tuesday.

See you soon,
Prof. Calloway