Unit 7

Structures of Quadratic Functions

Unit 7! Unit 7 is once again, all about quadratics. This time we are going to explore different properties of quadratic functions and look at different forms that their equations can have. There are pros and cons to each of these forms, so we are going to practice them until we become efficient at changing to forms that show us the features we are looking for.

Lessons 1 and 2

In lessons 1 and 2 we are exploring transformations. These first videos will take a look into how changing the equation of a quadratic function changes the graph. It is important to understand what the graph of a parent function looks like so we can determine what the graph of other functions look like. Some videos practice writing equations from a graph, and the some will practice writing equations from a table.

Quadratic Transformations Vertex Form Tutorial

Graphing Quadratic Functions Using Transformations

Writing vertex form given a graph

Writing Quadratic Equations in Vertex Form Using a Graph (THE EASY WAY!)

Writing Vertex Form from Table Example.mp4

I made this be nice

Vertex Form from a Table

Lessons 3 and 4

In lessons 3 and 4 we practice a method of switching between standard and vertex form called Completing the Square. Some videos are how we complete the square when a = 1, and the some are used if a ≠ 1.

Converting a Quadratic Function From Standard Form to Vertex Form (Completing the Square)

Convert Quadratic Function to Vertex Form by Completing the Square

Factor out a fraction to complete the square and find the vertex

Completing the square to transform from standard form to vertex form

Lesson 5

This is a practice lesson. Spend some time watching the videos in lessons 3 and 4 above for help.

Lessons 6 and 8 (7 is below)

These next videos will discuss the Sum-Product method of factoring trinomials. When we factor trinomials, we do so in order to find the x-intercepts of the function. The first two videos are used when a = 1 (Lesson 6), and the next two are used if a ≠ 1 (Lesson 8).

Ex: Factor Trinomials When A equals 1

Factoring a trinomial a = 1

Factoring Trinomials with Leading Coefficient not 1 (fast way)

Factoring Trinomials With Leading Coefficient not 1 - AC Method & By Grouping - Algebra - 3 Terms

Lesson 7

In Lesson 7, we did lots of practice of multiplying binomials. We covered the box method and the FOIL method earlier in this unit, but we are going to review them here. The videos below show each method.

FOIL Method for Multiplying Binomials - Distributive Property

Multiplying Binomials by the FOIL Method

MULTIPLYING BINOMIALS BOX METHOD TRICK

How to Multiply Binomials Using the Box Method

Lesson 9

In Lesson 9, we talked about more graphing of quadratic functions, but this time it was graphing when we are given factored form. Now we don't know the vertex, but we know the x-intercepts. These videos will show the steps we should use to create our graph from factored form.

Graphing Quadratic Functions in Factored Form

Graphing parabola from quadratic in factored form

Lesson 10

Another practice/cumulative lesson! Use the other lessons to practice your skills!

Lesson 11

In Lesson 11 we learned about solving quadratic equations. These video below will show how to solve by factoring, and how to solve when completing the square.

Ex: Factor and Solve Quadratic Equations When A equals 1

How to solve with factoring a quadratic equation when a=1

Solving a quadratic by completing the square

How to Solve by Completing the Square (NancyPi)

Lesson 12

In Lesson 12 we learned about the quadratic formula. This is used to find the x-intercepts of ANY quadratic function, whether it is factorable or not. Below are some examples, and some catchy tunes to remember it.

Factoring Trinomials with Leading Coefficient not 1 (fast way)

Factoring Trinomials With Leading Coefficient not 1 - AC Method & By Grouping - Algebra - 3 Terms

Quadratic Formula Pop Goes the Weasel

Extra Practice

This link is the same as Unit 6 and is still super helpful. The videos above also have tons of practice problems. You don't have to work through every section, just choose the ones that seem helpful for what you need to work on.

Quadratic functions & equations | Algebra 1 | Math | Khan AcademyWe've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems.

Unit 7 Assessment Review Video

Part 1

Alg U7 Review Vid Part 1.mp4

Part 2

Alg U7 Review Vid Part 2.mp4

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