Unit 2, Quadratic Functions: Day 13

Focus: Solving with the Quadratic Formula & Using the Discriminant

Action Items:

1. Show me yesterday's homework 2.11.

2. Take good notes on the QF and the discriminant!

3. Homework 2.12: BI p. 127 #1-4 all; 10-16 even; and 19-33 odd.

Lesson Goal: At the end of this lesson, you will be able to

- use the quadratic formula to solve any quadratic equation
- understand the connection between the discriminant and the number and types of solutions of a quadratic equation.

1. Notes (from yesterday):

$LaTeX: x\:=\:\frac{-\:b\:\pm\sqrt{b^2\:-\:4ac}}{2a}$

Must be in standard form, then identify $LaTeX: a,\:b,\:and\:c.$

2. Plug $LaTeX: a,\:b,\:and\:c$ into the Quadratic Formula.

3. We use the QF when the quadratic equation is

not in vertex form (when you have vertex form, it's simpler to solve using square roots)
not easily factorable in its standard form.

The Discriminant: the part of the Quadratic Formula that is under the radical (the radicand), $b^{2} - 4 a c$ is called the discriminant. The discriminant tells you what kinds of solutions you have (real or imaginary) and gives you information about when, how, and whether, the graph crosses, touches, or does not touch, the x-axis.

Analyzing the Discriminant-1.png

Practice in class.

2. Homework 2.12: BI p. 127 #1-4 all; 10-16 even; and 19-33 odd.

Resources:

Quadratic Unit Homework Solutions

Reminder: all of the resources can be found in the Quadratics Resources Module.

Also, try Patrick JMT Math Tutorials: All About Quadratics (Complete Playlist)

And if you like Kahn Academy, use their Quadratics unit if you need more support.