Unit 2, Quadratic Functions: Day 10

Focus: More Solving Quadratic Equations by Using Square Roots -- simplifying radicals, Day 3.

Action Items:

1. I will check Thursday's homework 2.8 (and your "HW Amnesty" work if you have any) tomorrow.

2. Take more notes on Solving Quadratic Equations using Square Roots by copying the examples below.

3. Homework 2.9: Solving Vertex Form (more practice). Do #1-8 on the "simplifying roots" side and all the problems that you can do on the other (we don't know how to do five of them -- can you tell which five?!).

4. Don't worry about the quiz from Friday for now. I have not decided what to do with them and have not finished looking at all of them.

Lesson Goal: At the end of this lesson, you will be able to (just more practice of both)

- solve a quadratic equation by using square roots and
- when this method is most appropriate (efficient).

Example 1: $LaTeX: 4\left(x\:-7\right)^2\:=\:80$

Think about it: why might it be important to be familiar with the perfect squares?! 😉

Example 2: $LaTeX: f\left(x\right)\:=\:\left(x+3\right)^2\:-16$

Think about it: how would your answer to example #2 change if the equation were $LaTeX: f\left(x\right)\:=\:\left(x+3\right)^2\:+16$

Example 3: $LaTeX: y\:=\:-3\left(x-5\right)^2\:+12$

Think about it: what form is this quadratic equation? what is its vertex? does that make sense with the solutions we got?

Example 4: $LaTeX: -2x^2\:-4\:=\:3x\:+\:5$

Think about it: make a generalization about when you use factoring versus when you solve by isolating the squared factor and taking a square root. What if neither method works? (Hint: this is when we'll use the Quadratic Formula)!

2. Some connections to graphing: looking for patterns. What do these parabolas look like graphically and what "kinds" of equations produce them?

Two real roots (also called solutions or x-intercepts)
One solution (also called root or x-intercept)
No real roots (i.e. the parabola does not cross the x-axis)

3. Homework: 2.9 Solving Vertex Form (more practice). Do #1-8 on the "simplifying roots" side and all the problems that you can do on the other (we don't know how to do five of them -- can you tell which five?!).

Preview of tomorrow: The Imaginary Unit: $LaTeX: \sqrt{-1}\:=\:i$ From this definition, and the way square roots work, we can also say that $LaTeX: i^2\:=\:-1$

The imaginary unit allows us to find solutions even if they are not "real." Non-real solutions do not cross the . Two imaginary solutions means your parabola is either above the axis and opening up, or below the axis and opening down.

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.