Week 7 · Readings & resources

Week 7 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 7 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 10 items (4 readings and 6 videos). Allow 65–77 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (19–22 min total)

① How do I get two answers from one equation? Factoring and the zero-product property

Chapter 7, Section “Factor and use the zero-product property” · Session 1, Segment 2, “Factoring and the zero-product property” · Remember: get 0 on one side, factor, and set each factor equal to 0; never divide both sides by x.

Solving Quadratic Equations by Factoring — Purplemath — a step-by-step page with several worked equations, a clear warning against dividing through by x, and a check of both answers by substitution. This builds on Week 6's work with factoring polynomials. (reading, 5–8 min)
❖ Solving Quadratic Equations by Factoring - Basic Examples ❖ — Patrick J — short worked examples of moving every term to one side, factoring, and setting each factor equal to zero. (video, 7 min) (captions: automatic)
Solving Quadratic Equations by Factoring — Mathispower4u — a calm run through several equations, including one where a common factor comes out first, which is the safe move instead of dividing by x. (video, 8 min) (captions: creator)

② What if one side is a square? The square root property and completing the square

Chapter 7, Section “Build a square: completing the square” · Session 1, Segment 4, “Completing the square” · Remember: take half of b, square it, and add that number to both sides.

Ex: Solve Basic Quadratic Equations Using Square Roots — Mathispower4u — a short example of taking the square root of both sides and keeping both the positive and the negative answer. (video, 3 min) (captions: creator)
Solving Quadratic Equations By Completing The Square — The Organic Chemistry Tutor — several equations in a row, each solved by moving the constant, adding the square of half of b to both sides, and finishing with a square root. (video, 8 min) (captions: automatic)
Completing the Square for Quadratic Equations — The Math Doctors — a long-running math help service starts with the easiest case, adding the square of half the x-coefficient to both sides, and then draws the square being finished as a picture; read the first two examples and skip the alternative methods later on. Use it while working through the Week-7 module overview. (reading, 8–12 min)

③ Which formula works every time? The quadratic formula and the discriminant

Chapter 7, Section “Use the quadratic formula on any quadratic” · Session 2, Segment 6, “The quadratic formula and the discriminant” · Remember: the whole top is divided by 2a, and the sign of b² − 4ac tells you how many real solutions to expect.

Quadratic Formula and Examples — MathBootCamps — two worked equations that first get 0 on one side, read off a, b, and c with their signs, and simplify the formula to an exact answer that keeps the radical; skip the closing part on complex solutions, because this course reports a negative discriminant as no real solution. (reading, 5–8 min)
Solving Quadratic Equations Using The Quadratic Formula & By Factoring - Algebra 2 — The Organic Chemistry Tutor — the same equations solved both by factoring and by the formula, so you can see the two methods agree. (video, 11 min) (captions: automatic)
Using the Discriminant for Quadratic Equations — Patrick J — how the sign of b² − 4ac predicts two real solutions, one repeated solution, or no real solution before you solve. (video, 7 min) (captions: automatic)

Optional one-stop reference (free online reference)

Quadratic Equation — Wolfram MathWorld — a mathematics encyclopedia's entry; read the opening definition of standard form and the formula built by completing the square, and skip the later material on history, numerical methods, and sums and products of roots, which goes beyond this course. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

Provenance: Built with The Course Maker · samples.thecoursemaker.com