Solving Quadratic Equations – Comparing and Contrasting Methods

April 21, 2015

After looking at your practice quizzes, here are the biggest misconceptions that I noticed:

• How do you factor when the leading coefficient (a) is negative?

• How do you determine the solutions to a quadratic equation from a graph?

• What are the differences between “factoring completely” and solving a quadratic equation?

• Remembering when taking square root of both sides of equation

• Writing quadratic formula and extending whole fraction bar underneath numerator

• Explaining differences between quadratic functions, quadratic equations, and the quadratic formula

• What do you do when one method doesn’t work?

There are 5 methods that you have learned for solving quadratic equations:

• Factoring• Completing the Square• Graphing• Taking the Square Root• The Quadratic Formula

Factoring

a = 1 Factor normally

or use British Method

a 1 Factor using

British Method

Solving Quadratic Equations: Factoring

• Solve the quadratic equation by factoring

Solving Quadratic Equations: Factoring Solve the equation by factoring:

Pros: Efficient and easyCons: It doesn’t always work if the roots are irrational

Completing the Square

a = 1 Complete the Square using

normal process

a 1 Divide all terms by a and then complete the

square

Solving Quadratic Equations: Completing the Square

• Solve the quadratic equation by completing the square:

Pros: It always works. Useful in upper level classesCons: Time-consuming and a lot of steps

Solving Quadratic Equations: Completing the Square (

• Solve the quadratic equation by completing the square:

Solving Quadratic Equations: Graphing

• Solve the quadratic equation by graphing with the TI-nSpire or TI-84 graphing calculator:

Pros: Quick, visual, easyCons: You won’t always have a graphing calculator. Difficult to estimate specific roots if roots are irrational

Solving Quadratic Equations:The Quadratic Formula

Solve the quadratic equation by using the quadratic formula:

Pros: It always worksCons: Time-consuming

Solving Quadratic Equations: Taking the Square Root

• Solve the quadratic equation by taking the square root

Pros: Quick and efficientCons: It only works when b = 0

It’s often going to be up to you to solve to choose a method for solving quadratic equations, especially on a college admissions test.

• What’s your plan if you try one method and it doesn’t work?

• How can you know for sure how many solutions a quadratic equation has?

• What, in your opinion, is the best method for solving quadratic equations?

Explain the difference between a quadratic equation, quadratic function, and the quadratic formula.

Up next this week and next week:• Today: Factoring by Completing the Square (cont’d)

and Deriving the Quadratic Formula• Tomorrow: Factoring by Guess-and-Check and

Review Difference of Squares/Perfect Square Trinomials

• Thursday: Factoring Word Problems• Friday: Factoring by Grouping and Distributive

Property and More Word Problems• Monday: Rotated Out• Tuesday: Review Day• Wednesday: Unit Test – Factoring, Solving Quadratic

Equations, and Polynomials

Team Challenge: Complete the Square on the General Case

For this group challenge, you and your team will attempt to complete the square on the general case of a quadratic equation

The specifics:• The first 4 minutes are independent work time so that

you can gather ideas, brainstorm a strategy, and prepare to work with your group.

• You will then have 7 minutes to complete the square with your group

The Prize:• Any group demonstrating their complete process and

correctly completing the square will earn a homework pass for tonight , Wednesday, April 23rd

Ready…Go!

Complete the Square on

Class Discussion: How do you complete the square on the general case

𝑎𝑥2+𝑏𝑥+𝑐=0

Factoring by (Grouping)April 22, 2015

This topic should be familiar – you have already factored by grouping with the British Method!

*The basic idea is to group terms with “common factors” before factoring

Example 1: Factor

Example 2: Factor

Example 3: Factor

Sum and Difference of Cubes Patterns

• Two other special factoring patterns!

Helpful memory trick:

Example 4:

Example 5: Factor

Example 6: Factor

Small-Group Work: Please complete today’s worksheet with your group.