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