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Week 7 · Module overview

Week 7 — Quadratic Equations

College Algebra Free sample edition

Welcome to your Week 7 Start Here page.

Why this matters

A quadratic equation is how a sports analyst finds when a kicked ball comes back down and how a landscaper sizes a patio to cover a set area. Solve it, then check which answers fit.

In plain language

This week you solve equations where the unknown number is multiplied by itself, which is called squared (written with a small raised 2, as in x²). Those equations usually have two answers instead of one, and you will learn four ways to find both. You will also learn to read one small number, the discriminant (the part of a formula that tells you how many real answers to expect), before you do any solving. Every answer you find, you will check by putting it back into the original equation. When an equation describes something real, such as a ball landing, you will also decide which answers make sense.

  • Already covered: Week 1 set the exponent and sign rules; Week 2 solved linear equations; Weeks 3 to 5 built functions, lines, and systems; Week 6 multiplied and factored polynomials.
  • This week: solving quadratic equations by factoring, the square root property, completing the square, and the quadratic formula, plus the discriminant.
  • How they connect: every factoring move this week is a Week 6 move, and every equation step is a Week 2 move done to both sides.
  • Where we're going next: Week 8, Midterm Review & Exam, reviews Weeks 1 to 7 by the one core move each topic asks for, and then comes the midterm.

Focus

When the unknown is squared, how do you find every answer, and which answers does the real situation keep?

By the end of this module, you should be able to:

  • [ ] solve a quadratic by factoring without dividing by x
  • [ ] use the square root property and complete the square
  • [ ] use the quadratic formula and read the discriminant
  • [ ] reject an answer the setting rules out

To-do

Plan your week

  1. Read Chapter 7 (about 45 minutes), then the lecture and slides.
  2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
  3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
  4. Take the quiz.

This week's checkpoint: solve x² − 6x + 5 = 0 two different ways and check both answers.

You've got this

Take it in order, and ask your instructor early if a step snags.

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