Week 9 — Readings & Resources · Quadratic Functions & Their Graphs

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
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.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~3 readings + ~2 videos, grouped by the three ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 35–50 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the parabola & vertex form → ② standard form & the vertex formula → ③ intercepts, discriminant & applications.

A habit to carry forward: the AI tutorial this week ends by having you catch a chatbot's mistake on a vertex sign. Keep that posture as you read — the tool drafts, you check.

① The Parabola & Vertex Form

Maps to Lecture Segments 1–2. Every parabola has a vertex; vertex form f(x) = a(x − h)² + k makes the vertex (h, k) a direct read — but watch the sign of h.

Reading — "Quadratic Functions" (OpenStax, College Algebra 2e, §5.1)
🔗 https://openstax.org/books/college-algebra-2e/pages/5-1-quadratic-functions
Why it's assigned: the section opens with vertex form, walks through reading h and k directly, and shows how a determines direction and min/max — exactly the arc of Segments 1 and 2. The "Recognizing Characteristics of Parabolas" and "Finding the Domain and Range of a Quadratic Function" subsections are the core read.
⏱ ~12 min

② Standard Form & the Vertex Formula

Maps to Lecture Segment 3. Standard form f(x) = ax² + bx + c hides the vertex; the formula x = −b/(2a) finds it. Watch the sign — always write the minus first.

Reading — "Parabolas" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/parabolas.aspx
Why it's assigned: a tight, example-packed page that covers vertex form and standard form side by side, works through multiple examples of x = −b/(2a), and diagrams the vertex, axis, and intercepts on the same sketch. A great second pass after the OpenStax reading.
⏱ ~10 min

③ Intercepts, Discriminant & Applications

Maps to Lecture Segments 5–7. The discriminant tells you how many x-intercepts exist before you solve; applications (projectile, optimization) always live at the vertex.

Video — "Graphing Quadratic Functions" (Professor Leonard — Precalculus / College Algebra 24)
🔗 https://www.youtube.com/watch?v=VH4tzzBVbgA
Why it earns the click: a full-length, board-worked lecture covering the parabola shape, vertex in both forms, intercepts, and the meaning of the discriminant — unhurried and step-by-step, the same style as the in-class lecture. Ideal if you want to see every step worked out.
⏱ longer lecture (skim to the parts you need; the vertex and intercept sections are in the first half)

Video — "Finding the vertex of a parabola in standard form" (Khan Academy)
🔗 https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/ex3-completing-the-square
Why it earns the click: a short, focused worked example using x = −b/(2a) — good for a quick review of the vertex formula before the quiz. Pairs well with the OpenStax and Paul's readings above.
⏱ ~8 min

Optional one-stop references (free online)

If you'd like references you can return to all term, Paul's Online Math Notes — Algebra has a full, free set of notes, and Professor Leonard's Precalculus / College Algebra playlist covers every topic in this course in full-length lectures.
🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP
Why they're here: reputable, currently-available references you can come back to in later weeks — entirely optional this week.

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §5.1 — Quadratic Functions (group ①, vertex form and direction).
2. Read Paul's Online — Parabolas (group ②, standard form and x = −b/(2a)).
3. Watch Khan Academy — Vertex in standard form (group ③, short worked example).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes reference above in the meantime.