In this post, we will discuss how to sketch the graphs of 
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 
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