# Solving Quadratics

### Alannah Goode

## You can Solve by Factoring...

## ...Or by using the Quadratic Formula

## Complex Numbers

## Adding Steps: 1) Add like terms | ## Subtracting Steps: 1) Distribute the "-" sign to numbers in last parentheses 2) Combine like terms | ## Multiplying Steps: 1) Use FOIL method (First, Outer, Inner, Last) 2) Remember: i² = -1 3) Combine like terms |

## Dividing

1) If needed, multiply by conjugate (switch "+" or "-" sign)

2) Multiply using FOIL method

3) Remember: i² = -1

4) Combine like terms

5) Reduce if possible

## Graphing Quadratics

## Standard Form

## Vertex Form

## Application Problems

## Maximum/Minimum Problems

**Example:** A hot air balloon takes off from the ground. The height in meters, h, of the hot air balloon above the ground is given by h = -6t² + 60t + 130. *t* is the time in seconds. Find the maximum height of the hot air balloon in the air.

1) To find the time of the maximum height, plug the numbers into the vertex formula; reduce if possible.

2) Now that you have the time, you need to find the maximum height. Plug the vertex into the original equation so it takes the place of *t*.

## Time at which an object hits the ground

**Example: **The height in feet, h, of a penny thrown into the air is given by h = -8t² + 50t + 130. *t* is the time in seconds. Find the time it takes the penny to fall to the ground.

1) You need to set h = 0 and solve for *t* for this problem, as it wants to know the time it takes the penny to fall to the ground.

2) Plug your numbers into the quadratic formula and solve, and reduce if possible.

3) In the end, you will have a positive and negative answer. Only the positive answer is correct because you can't have a negative time.