# All About Quadratics

### Standard Form

## By: Suhasee Patel

## Learning goal 2

The **quadratic formula** is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. Using the quadratic formula is often the most convenient way.

Here x represents an unknown, while a, b, c and are constants with a not equal to 0. One can verify that the quadratic formula satisfies the quadratic equation, by inserting the former into the latter. Each of the solutions given by the quadratic formula is called a root of the quadratic equation.

Geometrically, these roots represent the x values at which *any* parabola, explicitly given as y=ax^2+bx+c crosses the -axis.

## Learning Goal 3

For Example:

## Summary

## Quadratic Formula

*ax²+bx+c,*can be solved using the quadratic formula. It is used by substituting the values of

*a, b and c*from the original equation, into the formula, then solving.

By using this formula it is easier to solve for the solutions or the roots of the quadratic equation. This is a another way to solve an equation if it cannot be factored.

Here are the steps on how to solve the formula:

## Discriminant

*b^2 -4ac*

## 2 solutions/ x-intercepts If the D value is greater than 0 there will be 2 solutions/ x-intercepts. D>0 | ## 1 solutions/ x-intercept If the D value is equal to 0 then there will be 1 solution/ x-intercept. D=0 | ## 0 solutions/ x-intercepts If the D value is less than 0 so negative then there will be no solution/ x-intercept. D<0 |

## 2 solutions/ x-intercepts

## 1 solutions/ x-intercept

## Word Problems

__Revenue Word Problems:__

Revenue = (Current price +/- Price decreased/increased X) (Current sales parameters +/- Number parameters decreased)

- For example, If Bill Gates sells 15 copies a day of Windows 7 at the current price of $299, he would sell 4 more copies of Windows 7 per day if the price decreases $5.
- X will be the amount of times increased in the price.
- Equation would be: Revenue = (299-5X)(15 + 4X)
- The amount you increase will be X.

For Example:

__Geometry Word Problems:__

- Helps us find the unknown lengths of the shape.
- We can use the quadratic formula in order to solve it
- Most of the time when we solve it we will get a positive and a negative number, so we should always use the positive number to sub into the the original equation because the length can never be negative!

For Example:

## Reflection

The Standard Form unit test was the test that I did fairly well on, and many people had said that it becomes easy once you understand it. I also figured out that once you begin to understand vertex form and factored form standard form becomes much easier. The unit that I had some difficulty on was factoring because at first it was hard to remember the different ways to factor but after constantly doing my homework it began to make more sense to me.

Some connections that I have made throughout the quadratics unit is how when we factor the equations it can help us graph the parabola and find the vertex, x-intercepts and y-intercepts. Also if we use the quadratic formula we can solve for x and then we can graph the equation while in vertex form.