In this post, we will discuss how to sketch the graphs of , for y=-2 to 3.

First, we will look at Quadratic Graphs ()

## Quadratic Graphs

If a>0, the graph is a “U” shape or “happy face”. 🙂

If a<0, the graph is a “n” shape or “sad face”. 😦

## Intercepts

- To find x-intercept: Let y=0
- To find y-intercept: Let x=0

## Completing the square

- E.g. (take out common factor of )
- = (
**Key step: Divide coefficient of x by 2, add & subtract the square of it)** **Check your answer using substitution method!**(Sub. in into your initial and final answer)

## Turning Points

* (p,q) is the turning point of the graph

For example,

**Minimum pt: (2,3)**

## Graphs of

### , where a>0 (Volcano shape)

Not touching the x-axis (Asymptote)

If a<0, the graph becomes upside down.

()

### , where a>0. (Hyperbola, Slanted Hourglass)

If a<0, it will be upside down (reflected about x-axis)

()

### Cubic