7.7 - Quadratic Equations and Functions

Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on solving quadratic equations and graphing quadratic functions.

Common Core State Standards:

A-REI.1
A-SSE.3
F-IF.1
F-IF.2
F-IF.7
F-IF.8
F-IF.9

Learning Objectives:

To review the relationships between the concepts of equation, function, and graph and apply them to the context of quadratics.
To understand the zero-product property.
To learn how to solve a simple quadratic equation.
To learn the shape of the graph of a quadratic function.
To learn how to graph a quadratic function.

Guiding Questions:

What is an equation?
What is a function?

Can you give an example of a function with infinitely many elements in the domain and infinitely many elements in the range?
Can you give an example of a function with infinitely many elements in the domain and just one element in the range?

What is the difference between an equation and a function?
What is a linear equation?
What is a linear function?
What is a quadratic equation?
What is a quadratic function?
What does it mean to solve an equation?
How do we solve $x^2=6-x?$
What can we say about the equation ab = 0, where a and b are real numbers?
How do we graph $f\left(x\right)=x^2+x-6?$ $f\left(x\right)=x^2+x-6?$
What are the x-intercepts? How many are there?
How many y-intercepts are there? Why?
How do you solve $x^2=1?$
Graph $f\left(x\right)=x^2-1$ $f\left(x\right)=x^2-1$
Graph $f\left(x\right)=x^2+1$ $f\left(x\right)=x^2+1$
What do you notice in those two graphs?

Notes for Teachers:

Ask for examples of equations and functions every time you ask the questions above. Also, clarify that although at this level and in many textbooks the terms quadratic equations and quadratic functions are used interchangeably, they are different objects.

Video of the Day:

7.7.1 Quadratic Equations or Quadratic Functions?

This video shows the relationship between quadratic equations and quadratic functions, clarifying some general misconceptions.

7.7.1 Quadratic Equations or Functions.-1.mp4 Download 7.7.1 Quadratic Equations or Functions.-1.mp4 Play media comment.