# Math

### Quadratics relations, expressions, and equations

__x y__

1 -4 Quadratic relations is using the information you get from a table or

0 -1 equation and graphing it to get a visual example. You can also use

-1 0 the vertex and the points on the graph to make an equation.

-1 -1

-2 -4

In quadratics you will need to know how to make a graph into a chart and a chart into a graph. You will also need to know the axis( the x and y of the highest or lowest points), The axis of symmetry( the center of the two zeroes of the line). This helps you understand the quadratic equation because it gives you a visual representation of what the equation represents

To multiply polynomials you first need to expand using the distributive properties. Then you need to add the common factors. After you use the distributive property to expand the equation you can simplify the equation by adding the properties of the equation that can be added.

For special products you need to expand your equation then use the distributive properties method. You cant change an equation into factored form if nothing can be multiplied so you have to expand the square to make it possible to expand into something that can be multiplied than you can simplify the equation by adding common factors.

To solve the equation you need to find the greatest common factor then you need to factor it in to the equation. To use this method find the GCF of the two than factor the GCF into the equation making the equation simpler to understand and solve.

To use the a+bx+c method first you need to multiply ac in this equation I got 5. To solve this equation you must find numbers which when multiplied equal 5 and added up equal 6. After you get the two numbers you then factor the first two then the second two. Then you make an equation where the two numbers you used for factoring and the two remaining attributes are added and then multiplied.

For a+bx+c a had a value of 1 in this equation a has a value of two. In this equation I factored out x to get ride of the squared. When a has a value larger than one it makes the ac value a lot bigger making it hard to find the number that is when added equal to the b value and when multiplied is equal to the ac value.

## Perfect square trinominal

If the parts of the equation all are able to be squared then to reduce the value and to expand you will need to do this. This equation was not possible to expand more. Because in this equation we had two numbers that are squared we can double the value and multiply them with each other.

For this formula a calculator is mandatory. You need to find a,b, and c and replace them into the formula above. then you solve to find the numerator until you have -b+- (the other number). Then you use the +- for two alternatives in one the numbers get added in the other they get subtracted. Then you solve the numerator then divide the two alternative equations with the numerator two get your two x-intercepts. This method is only recommended when the ax+bx+c method is impossible to use.

## End

This Smore covers the important parts of the quadratics unit and gives you a demonstration of what quadratics is. Quadratic is a really hard subject and takes time to learn so I hope that this Smore helps with that