# Quadratic Relationships

### Summerzing the entire Quadratics

## The topics that i have learned in Quadratic Relationships:

- Analyzing Quadratics
- Finding the given equation
- Determine the equations from the graph
- Factoring

## Analyzing Quadrates

- Make table of values for x-intercept and y-intercept.
- If the first differences are equal, it would be considered as linear relationships.
- If the second differences which are equal, it would be considered as quadratic relationships.

## Finding the given Equation

- The vertex of this parabola is (-2,8). Add these two points in the vertex formula.
- There is also a given x-intercept which is (2,0). To make an equation, Insert these two points to the same formula and make an equation by solving it..

## Determine equations from the graph

- If the parabola open downwards, it means the "a" will be negative.
- To find the "a" value, The parabola passes through the point (0,2). So substitute these two points in the same formula and solve it by the BEDMAS method.

## Part 2

## Expanding

- we have given the equation in the factor form so we have to expand the equation and simplify it.

## Common Factoring

## Factoring By Grouping

- in this equation find two common pairs.

## Factoring Simple Trinomials

-The big two boxes are known as X square, the long two bars are the x's and the tiny little squares are the numbers and in each pair one is negative and the other one is positive.

- In this equation, Multiply 2 with everything inside the bracket.- Add 2 tiles in the length side.

- Add 3 tiles at the width side.

- Fill all the areas.

## Factoring Complex Trinomials

- also, the x square has a number with it so we wanna make it sure if we are solving the equation in a proper way.

## Factoring Special Trinomials- Difference of Squares.

In complex problem, we find the GCF and then put it the factor form.

## Perfect squares

## PART 3

## Completing the Squares

## Solving Quadratic Equations

## Solving Standard Form Equations

- we use this formula to find the x's, axis of symmetry which is our x-int and an optimal value which is known as y-int. This will be our vertex if we graph it.

## Quadratic Word Problems

- To find the solution, we solve the quadratic problem by using the Quadratic formula!