This week I learned many cool and fascinating facts about the general form of a quadratic equation ( 
General form
- Positive – Open upward
- Negative – Opens downwards
bx:
- is a mixture of both
and bx so it can differ
c:
- Is the y axis
Analyzing equation:
using this formula can tell us a lot of things that will help us graph the equation. In fact it will tell us 8 helpful clues.
ex. $latex -2(x+2)^2 – 1
- Vertex: the vertex will be p and q … (-2,-1) * p is always backwards from the formula because in the original equation it is (x – p) therefore it has to be a negative number for it to become positive in the new equation.
- Axis of symmetry: This will be p because it is the x value on a graph …-2
- Opens up or down: This is determined if
- If it is congruent to
. This means that the pattern of the graph would be 1, 3, 5. Meaning 1 over 1 up, 1 over 3 up, 1 over 5 up etc. If it does not follow the 1,3,5 rule it means that a has a value different from -1 or 1. Say a = 4, multiply 4 to each number from the original pattern. ex/ 1,3,5 is now equal to 4, 12 , 20 etc. This pattern will also tell us if the parabola will be stretched or compressed. If 1> a < 0 ( fraction ) it means that the parabola will be compressed. If 1 < a > 1 it means that the parabola will be stretched…. this equation is congruent to y =
, it is being stretched because 2 > 1, it is negative so it will be flipped upside down but the structure is the same. (congruent)
- Minimum or maximum: If a is positive, it will have a minimum. If a is negative it will have a maximum… It has a maximum of -1
- Domain. We know the XER because the parabola never ends.
- Range: If a is positive y will be greater than the minimum. If a is negative, y will be smaller than the maximum… y < -1, yER
IMPORTANT
$latex y = 3x^2 (x – 3)^2 + 4
The horizontal translation will be 3 units to the right even though it says -3.
I also learned that general form can be turned into the analyzing equation of 
Here is a video that helped me understand how to complete the square
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