Week 9 · Readings & resources

Week 9 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 9 (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 66–78 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 (20–22 min total)

① Where is the turning point? Reading vertex form

Chapter 9, Section “Read vertex form: the vertex in plain sight” · Session 1, Segment 3, “Vertex form and the sign of h” · Remember: in a(x − h)² + k the vertex is (h, k), and the number inside the parentheses comes out with its sign reversed.

Vertex Form of Parabola — ChiliMath — reading the vertex (h, k) straight from vertex form, with special care for the sign of h, how the sign of a decides whether the vertex is a minimum or a maximum, and a last example that converts a standard-form quadratic to vertex form by completing the square; if time is short, skip the middle examples that build an equation from a vertex and a second point. (reading, 8–12 min)
Graphing Quadratic Functions In Vertex Form — The Organic Chemistry Tutor — several parabolas graphed from vertex form, each one starting from the vertex and using the sign of a to decide which way the curve opens. (video, 8 min) (captions: automatic)
❖ Maximum and Minimum Values of Quadratic Functions ❖ — Patrick J — a short walkthrough of deciding whether the vertex gives a minimum or a maximum and reading off that value. (video, 4 min) (captions: automatic)

② How do I find the vertex when the formula hides it? Standard form, intercepts, and converting

Chapter 9, Section “Find the vertex from standard form” · Session 2, Segment 5, “The vertex formula and the intercepts” · Remember: find h with −b ⁄ (2a), then put h back into the function to get k.

Graphing Quadratic Equations — Math is Fun — the gentlest page here: it rewrites a quadratic in vertex form, reads the vertex and the mirror line, and shows how the number in front of x² squeezes or flips the curve; use it while working through the Week-9 module overview. (reading, 8–10 min)
Introduction to Quadratics, including the Quadratic Formula — Math Hints — a tutor's guide whose opening sections compare standard, vertex, and factored form, use the sign of a to tell a minimum from a maximum, and find the vertex from standard form with the vertex formula; read through the part on graphing with standard form and skip the calculator and regression sections. This builds on Week 7's work with solving quadratic equations. (reading, 8–12 min)
Graphing Quadratic Functions in Standard Form (Vertex Form) — Mathispower4u — a calm run through finding the vertex, the axis of symmetry, and the intercepts of a quadratic given in standard form, then sketching the graph. (video, 9 min) (captions: creator)
Convert from Standard Form to Vertex Form of a Quadratic (Parabola) 2 Methods — Mario's Math Tutoring — the same conversion done two ways, by completing the square and by the vertex formula, so you can see both land on the same vertex form. (video, 7 min) (captions: automatic)

③ How high, how much, how big? Maximum and minimum problems

Chapter 9, Section “Solve maximum and minimum problems” · Session 2, Segment 8, “Maximum and minimum problems” · Remember: write the quantity as a quadratic function, find the vertex, and answer with both coordinates and their units.

A Projectile Problem Using Quadratics - Example 1 — Patrick J — a short worked launch problem that finds when an object is highest and how high it goes from the vertex. (video, 3 min) (captions: automatic)
Ex: Quadratic Function Application - Maximum Area — Mathispower4u — a fencing problem that writes the area of a rectangle as a quadratic function of its width and finds the largest area at the vertex. Stop here before end behavior of higher-degree polynomials; next week takes that up. (video, 8 min) (captions: creator)

Optional one-stop reference (free online reference)

Parabola — Wolfram MathWorld — a mathematics encyclopedia's entry on the curve itself; read the opening description of the shape and skip the focus-and-directrix geometry, the polar equations, and the history, which go 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.

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