### By: Jasmit Dhonaha

On this flyer/website you will learn different ways to solve equations using quadratics. You will learn the types of equations (vertex form equations, standard from equations, and factored form equations), how to find things on your graph (axis of symmetry, optimal value, transformations, x-intercept, and step patterns), how to use algebra tile, how to solve common factors, simple trinomial, complex trinomial, difference of squares, perfect squares,and many more.

Types of Eqautions

• Vertex Form
• Factored Form
• Standard Form

Vertex Form

• Axis of symmetry
• Optimal Value
• Transformations
• X-Intercept
• Step Pattern

FACTORED Form

• Expanding and Simplifying
• X-Intercept
• Axis Of Symmetry
• Optimal Value

Standard Form

• Solving Equations using Algebra Tiles
• Common Factors
• Simple Trinomials
• Complex Trinomials
• Perfect Squares
• Difference in Squares

Word Problems

• Motion Word Problems
• Number Problems

Summary

• Desmos

## Types of Equations

Vertex Form- a(x-h)²+k

Factored Form- a(x-r)(x-s)

Standard Form- ax²+bx+c

## Graphing For The Axis of Symmetry

The axis of symmetry is very easy to do and will not take more than two minutes to find out. The axis of symmetry will divide your parabola in half. The axis of symmetry is the y value of your vertex. They way you find out the axis of symmetry is by first getting your vertex and the vertex is your h,k value. After you have done this you make a table of x and y. To get the value of y you subsitute the x value and put it in your equation. After you have completed your chart you can put in all your points to a graph. When you have done this you find the axis of symmetry by the y value of the vertex. For a example please look at the picture below it will tell you step by step of how to solve.

## Optimal Value

Optimal value are easy to notice. The optimal value is the y point of the vertex. If you have a equation that looks like this, y=a(x-h)²+k the optimal value is y=k. So if the equation is y=k you take your k value from the longer equations and plug it into y=k:

Example: y=a(x-2)²+4 - y=k - y=4

Therefore y=4 is your optimal value in this situation

## Transformations

Transformations are simple and very easy to do.

The (-h) moves the vertex of the parabola left or right. When the (h) is negative move right and when the h in positive move right.

The (k) value moves vertex of the parabola up or down. When the (k) value is negative you move down and when it's positive you move up.

The (a) value stretches the parabola. If (a) is negative the parabola goes down and if it is positive it goes up.

Vertex is always your (h,k) value.

After this you can use the step pattern to find the rest.

## X-Intercepts

X-intercepts are easy easy to find. X-intercepts are the points/point that hits you X line. You can either have one or two intercepts. The way to find the X intercepts are very easy. If you want to know how to get the x-ingtercepts look at the two examples below one example will show you just one x-intercept and the other example will show you two x-intercepts.

## Step Pattern

Step patterns are used to find the other points that you are going to put on your graph. The step pattern is 1, 3, and 5. For an example of how the step pattern is used in a vertex form equation please look at the example video posted below.

## Expanding and Simplifying (Factored To Standard)

This is method of turning equation to its normal state. This is very simple and takes a small amount of time to do. First you look at your equation you times your first number in the first bracket with the first number in the second bracket. Then you times the first number in your first bracket with the second number in the second bracket. After you times the second number in your first bracket with your first number in your second bracket. Then you times the second number in the first bracket to the second number in your second bracket. Finally you grab your like terms to get a final answer. For a example of expanding and simplifying watch the video posted below.

## X-Intercepts

The x-intercepts are the point/points that hit your x line. You can either have one or to x-intercepts. The way you find out is by looking at you parabola and find the points on your graph that hit the x-intercepts.

## Axis of Symmetry

The axis of symmetry is easy to find out. The axis of symmetry divides your parabola in half. The axis of symmetry is your y value of your vertex. If you want a example of how to get the axis of symmetry watch the first video that comes up below.

## Optimal Value

The optimal value is like the axis of symmetry instead of getting the y value you need to get the x value. The optimal value is a horizontal line from your vertex. If you want to know how to get the optimal value please watch the video posted below.
3.5 Graphing from Factored Form

## Solving Using Algebra Tiles

Using algebra tiles might be the longest way of solving an equation but it's the easiest way. Algebra tiles are the best way because you can actually see if your equation is right. Algebra tiles don't take that much knowledge solve that why it the easiest. The video below will help you solve by using algebra tiles.

## Common Factoring

Common factors are fast to solve and are some what easy. They take more knowledge than algebra tiles but are more quicker to solve. The way to do common factors are by canceling out number. You can see in the video on below.

## Simple Trinomials

Simple trinomials are very fast and easy to solve. They way you solve simple trinomials is to first get the the factors to the last number (the number without a x value). When you list all the factors of the last number then you look at your factors and choose the one that you can add or subtract so it will equal your middle number. After you found the factors that equal your second number put it into this equation (x(+ or -)one of your factors) (x(+ or -)one of your factors). For an example you can look at the video posted below.

## Complex Trinomials

Complex trinomials takes more steps and are more hard to solve than simple trinomials. Complex trinomials are just like simple trinomials when solving but have a little different steps when solving. You can watch the video below it will tell you step by step how to solve a example of a complex trinomial.

## Perfect Squares

Perfect squares are easy and really quick to solve. Basically all you are trying to do is to make square perfect (all sides are the same value). Some ways to tell if a square is perfect is by the equation if both brackets have the same number as its ending its a perfect square.

Examples: (x+3)(x+3) or (x+3)²

If you want to know how to solve perfect squares please watch the video posted below.

## Difference of Squares

Difference of squares take knowledge to solve. The way you solve difference of squares is by square rooting your two terms and then putting it into a equation for the problem. If you want to know how to solve difference of squares please watch the video posted below.