Using the Quadratic Formula

Topics for Today:

One method that can be used to solve any quadratic equation is the quadratic formula.  The quadratic formula uses the coefficients from the equation to find the values for x when y is zero.  It is highly recommended that students MEMORIZE the quadratic formula.  The quadratic formula works even when we don't have real solutions (yes, there is such a thing as an imaginary number - stay tuned - you'll become very familiar with imaginary numbers in Algebra II). 

Vocabulary: quadratic formula

Sections Covered in Textbook:

10-2: Using the Quadratic Formula (pages 547-553)

Resources & Tutorials:

1) What is the quadratic formula?
2) How do you solve a quadratic equation using the quadratic formula?
3)  Using the Quadratic Formula class notes

Assignments:

Using the Quadratic Formula Worksheet

Factoring to Solve Quadratic Equations

Topics for Today:

All of the work we have done on factoring has led to today's topic of solving quadratic equations by factoring.  We talked about the zero-product property (when multiplying, if one factor is zero, then the equation equals zero), and how we use it to find our solutions (also called roots or zeroes). 

An example of an equation that requires several steps to solve is included here:

Vocabulary:  zero-product property

Sections Covered in Textbook:

10-5: Factoring to Solve Quadratic Equations (pages 536-540)

Resources & Tutorials:

1) What is the zero-product property?

2) How do you use the zero product property to find solutions to an equation?

3) How do you solve a quadratic equation by factoring?

4) Factoring to Solve Quadratic Equations class notes

Assignments:

Factoring to Solve Quadratic Equations Worksheet

Solving Quadratic Equations

Topics for Today:

Solving quadratic equations was the topic of the day.  We solved these equations by graphing and by using algebra.  For quadratic equations, we have three possibilities for our solutions:  we may have two solutions, one solution, or no REAL solutions.  The rules of algebra still apply when solving numerically - whatever we do to one side of the equation, must also be done to the other side to keep the truth of the equals sign.  Students were also reminded that squaring and taking the square root are inverse operations.

Sections Covered in Textbook:

10-4: Solving Quadratic Equations (pages 529-534)

Resources & Tutorials:

1)  How do you solve a quadratic equation with two solutions by graphing?

2)  How do you use the square root method to solve a quadratic equation with two solutions?

3)  Solving Quadratic Equations class notes

Assignments:

1) Solving Quadratic Equations Worksheet
2) Delta Math Weekly Review due by Friday at 3pm. 

Finding and Estimating Square Roots

Topics for Today:

Today we discussed perfect squares and square roots.  Squaring and taking the square root are inverse operations.  Students will be asked to memorize the common perfect squares, and there is a Quizlet set that should hopefully make learning them fun.

Vocabulary: square root, principal square root, negative square root, radical, radicand, perfect squares

Sections Covered in Textbook:

10-3: Finding and Estimating Square (pages 524-528)

Resources & Tutorials:

1) What is a perfect square?
2) How do you find the square root of a perfect square?
3) How do you find the square root of a fraction?
4) How do you estimate a square root of a non-perfect square?

5) Finding and Estimating Square Roots class notes

Assignments:

1) Finding and Estimating Square Roots Worksheet
2)  Weekly Delta Math review due Friday by 3pm

Quadratic Functions

Topics for Today:

Quadratic functions are still the topic of the day.  Today we worked with the axis of symmetry and used it to find our vertex.  Because parabolas are symmetric, we are able to find points on one side of the axis of symmetry and reflect them to the other side of the axis of symmetry.  Once we have the vertex, and a few points on either side of the axis of symmetry, we can easily draw our parabola.

Sections Covered in Textbook:

10-2: Quadratic Functions (pages 517-523)

Resources & Tutorials:

1) How do you find the axis of symmetry?
2) Find the axis of symmetry and your vertex
3) Quadratic Functions Class notes

Assignments:

Quadratic Functions Worksheet

Exploring Quadratic Graphs

Topics for Today:

Today we began our work on quadratic functions.  Quadratic functions, simply stated, are functions that have a variable with the highest degree exactly equal to two.  We looked at the standard form of a quadratic function and looked at graphs of different parabolas.

Vocabulary: quadratic function, standard form of a quadratic function, parabola, axis of symmetry, vertex, minimum, maximum

Sections Covered in Textbook:

10-1: Exploring Quadratic Graphs (pages 510-516)

Resources & Tutorials:

1) What is a quadratic function?
2) What is a parabola?
3) Class Notes - Exploring Quadratic Graphs

Assignments:

1) Exploring Quadratic Graphs Worksheet
2) Chapter 9 Test Corrections due Tuesday

Topics for Today:

Today we wrapped up our discussion of polynomials and factoring, and we discussed degrees of polynomials, names for them based upon the number of terms.  We also covered multiplying binomials and polynomials as well as factoring.  We did a class Kahoot to review for the test.  

Sections Covered in Textbook:

Chapter 9:  Polynomials and Factoring (pages 455-506)

Resources & Tutorials:

1) Chapter 9 Review Sheet

2) Chapter 9 Review Sheet Answers

Assignments:

Study for your test

Delta Math Optional Assignment is good for review as well.