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High School Algebra II: Tutoring Solution26 chapters | 274 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.

A **quadratic function** is a function or mathematical expression of degree two. This means that the highest power of the function is two.

All of the examples are of degree two. In other words, their highest power is two. Quadratic functions must have two as their highest power. It cannot be lower or higher. If it's lower or higher, it is no longer a quadratic.

Quadratic functions have a certain characteristic that make them easy to spot when graphed. They will always graph a certain way. Try graphing the function *x*^2 by setting up a t-chart with -2, -1, 0, 1, 2 to see what you get.

This particular shape is called a parabola. Quadratics will always graph into some form of parabola. They can stand upright like *x*^2 or they could be sideways if the variable is *y*. They can be located at different spots on the Cartesian plane, but they will always have a porabola.

The most common way of writing quadratic functions is in the standard form. In **standard form**, you write the terms in decreasing order such that the term with the highest exponent is first and the constant is last.

You will see standard form often. When making calculations on paper, this is the form that is usually given. In this example, *a* is 1, *b* is 5, and *c* is 6. There are, however, other forms.

Another form is called **factored form**, in which the roots or solutions of the quadratic equation are written as products to be multiplied.

All quadratic functions have two roots. The roots can be different or they can be the same. In this example, the two roots are -2 and -3.

And a third form that you can see quadratics in is called the **vertex form**, which is used when graphing a quadratic.

In vertex form, the *h* and the *k* give you the *x* and *y* coordinates of the vertex, respectively. In this example, the coordinates of the vertex are (2, 2).

The **quadratic formula** is used to help solve a quadratic to find its roots. In order to solve a quadratic function, you must first change it to a quadratic equation by setting the function equal to zero. Once you have done so and the quadratic is written in standard form, you can use the quadratic formula to find the two solutions.

Using the quadratic formula involves plugging in values from the standard form of our quadratic equation. You would plug in the respective values for *a*, *b*, and *c*.

**Quadratic functions** are all of degree two and all graph to a parabola. The three forms that quadratic functions can be written in are **standard form, factored form**, and **vertex form**. The standard form is the most common way of writing quadratics. Factored form gives you the roots of the quadratic. Vertex form is used when graphing quadratics. To solve a quadratic in standard form, the quadratic formula is used.

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High School Algebra II: Tutoring Solution26 chapters | 274 lessons

- Using Tables and Graphs in the Real World 5:50
- Scatterplots and Line Graphs: Definitions and Uses 7:17
- What is a Parabola? 4:36
- Parabolas in Standard, Intercept, and Vertex Form 6:15
- Multiplying Binomials Using FOIL and the Area Method 7:26
- Multiplying Binomials Using FOIL & the Area Method: Practice Problems 5:46
- How to Factor Quadratic Equations: FOIL in Reverse 8:50
- Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient 7:35
- Solving Quadratic Trinomials by Factoring 7:53
- How to Complete the Square 8:43
- Completing the Square Practice Problems 7:31
- How to Solve a Quadratic Equation by Factoring 7:53
- Formula for Finding the Area of a Parallelogram
- Quadratic Functions: Examples & Formula 3:56
- Go to Algebra II - Graphing and Factoring Quadratic Equations Review: Tutoring Solution

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