About This Chapter
Below is a sample breakdown of the Quadratic Functions: Precalculus chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Parabolas||Linear function, quadratic function, maximum height, vertex, roots, intercepts, axis of symmetry, minimum vertices, concave up or down, intercept form, standard form, vertex form, and the equations for each parabola form|
|Tuesday||Factors and factoring||The product, the factors, binomials, quadratic expressions, leading coefficient, distributive property, F.O.I.L in reverse order, coefficient, and pattern adjustment|
|Wednesday||Completing the square||Perfect square binomial, vertex form, changing c-values, inverse operations, standard form, and trinomials|
|Thursday||Solving and graphing||Complex numbers, imaginary numbers, discriminant, zero product property, standard form, the use of b^2 - 4ac, quadratic inequality, point plotting, the line, graph shading, system of quadratic inequalities, and the solution area|
|Friday||Application and modeling||Quadratic functions, f(x) = ax^2 + bx + c, the use of different coefficients, optimization problems, data sets, real-life mathematical models, and applying quadratic functions to different real-world situations|
1. What is a Parabola?
A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.
2. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
3. How to Factor Quadratic Equations: FOIL in Reverse
So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.
4. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!
5. How to Complete the Square
Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.
6. Completing the Square Practice Problems
Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!
7. How to Solve a Quadratic Equation by Factoring
If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!
8. How to Solve Quadratics with Complex Numbers as the Solution
When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!
9. Graphing & Solving Quadratic Inequalities: Examples & Process
When you finish watching this video lesson, you will be able to graph and solve your own quadratic inequality. Learn what steps you need to take and what to watch for.
10. Graphing a System of Quadratic Inequalities: Examples & Process
What is a system of quadratic inequalities? What are the steps to graphing them? Find the answers to these questions by watching this video lesson. When you finish, you will be able to graph these yourself.
11. Applying Quadratic Functions to Motion Under Gravity & Simple Optimization Problems
Quadratic functions are very useful in the real world. Watch this video lesson and learn how these functions are used to model real world events such as a falling ball.
12. Using Quadratic Functions to Model a Given Data Set or Situation
Watch this video lesson to learn how quadratic functions are used to model situations and data gathered from real world scenarios. See how our function fits our data and situation well.
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Other chapters within the High School Precalculus Syllabus Resource & Lesson Plans course
- Linear Equations: Precalculus Lesson Plans
- Inequalities: Precalculus Lesson Plans
- Absolute Value Equations: Precalculus Lesson Plans
- Complex Numbers: Precalculus Lesson Plans
- Systems of Linear Equations: Precalculus Lesson Plans
- Mathematical Modeling: Precalculus Lesson Plans
- Solving Quadratics: Precalculus Lesson Plans
- Geometry Basics for Precalculus Lesson Plans
- Functions: Precalculus Lesson Plans
- Function Operations: Precalculus Lesson Plans
- Graph Symmetry: Precalculus Lesson Plans
- Graphing with Functions: Precalculus Lesson Plans
- Rate of Change: Precalculus Lesson Plans
- Polynomial Functions: Precalculus Lesson Plans
- Advanced Polynomial Functions: Precalculus Lesson Plans
- Rational Functions & Difference Quotients: Lesson Plans
- Rational Expressions & Function Graphs: Lesson Plans
- Exponential & Logarithmic Functions: Lesson Plans
- Trigonometric Functions: Precalculus Lesson Plans
- Trigonometric Graphs: Precalculus Lesson Plans
- Solving Trigonometric Equations: Lesson Plans
- Trigonometric Identities: Precalculus Lesson Plans
- Trigonometric Applications: Precalculus Lesson Plans
- Graphing Piecewise Functions: Precalculus Lesson Plans
- Vectors, Matrices & Determinants: Lesson Plans
- Mathematical Sequences & Series: Lesson Plans
- Sets in Algebra: Precalculus Lesson Plans
- Analytic Geometry & Conic Sections: Lesson Plans
- Polar Coordinates & Parameterizations: Lesson Plans
- Continuity: Precalculus Lesson Plans
- Limits: Precalculus Lesson Plans