Week 9 — Quadratic Functions & Their Graphs

Welcome to your Week 9 Start Here page.

Why this matters

A parabola's vertex is how a sports analyst finds the top of a ball's flight and how a small-business owner finds the best price. Find it, and you can answer how high or how much.

In plain language

An object launched from an 80-foot platform climbs for 2 seconds, stops for an instant at 144 feet, and comes back down. This week you learn to read that kind of rise-and-fall from a formula, before you draw a single point. The curve it makes is a parabola (a U-shaped curve that is the same on both sides of a middle line). Its top or bottom point is the vertex (the turning point, where the curve stops going one way and starts going the other). Once you can find that point, you can answer questions such as how high, how much, and how big.

• Already covered: Week 3 named functions and their range; Week 4 found intercepts; Week 6 multiplied and factored polynomials; Week 7 solved quadratic equations and read the discriminant.
• This week: the quadratic function and its graph — the parabola, vertex form, standard form, the vertex formula, intercepts, converting between forms, and maximum and minimum problems.
• How they connect: a quadratic function's x-intercepts are the Week 7 solutions, its y-intercept is the Week 4 idea, and its vertex is a Week 3 function value.
• Where we're going next: Week 10, Polynomial & Rational Functions, reads graphs of higher-degree polynomials and fractions of polynomials from their formulas.

Focus

Where does a parabola turn, and what does the turn mean?

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

• [ ] read the vertex and the axis of symmetry from vertex form
• [ ] find the vertex from standard form and call it a minimum or a maximum
• [ ] find the intercepts and predict the x-intercepts with the discriminant
• [ ] convert between forms and solve a maximum or minimum problem

To-do

Plan your week

1. Read Chapter 9 (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: find and check the vertex of x² − 6x + 5, and say whether it is a minimum or a maximum.

You've got this

Take it step by step, and ask your instructor early.

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