Quadratics 4 Dummies!
y=a(x-h)^2+k
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a= The co-efficeient of the equation. So to break it down, "a" is what determains whether or not the parabola will be opening up or down in a U shape due to the stretch or compression. If "a" is positive it opens up and if its negative it opens down.
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h= The x value. This is what determains how much to the left or right your vertex will be. The vertex is the highest or lowest point on your parabola. Now heres where it gets tricky but I guarantee you can handle it. All it is, is that what ever number is given, it is the opposite value. So a positive number would be a negative and a negative would be a positive number. This is because if h=2 then you would need to move it 2 to the left therefor moving it to what I call "the dark side" in other words the negative side.
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k= The y value represents the y value. This determains how high or low the vertex of the parabola will be. There is not trick to this one, basicaly what ever the number is, it stays the same. Also is its positive the vertex will move up and if its negative it will move down. I know right, so easy!
* The h and k come together to form a corrdinate. For example,
y=4(x-9)^2+5
The corrdinate would be (9,5) and thats where your vertex would be.
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^2= Just means that the equation is a parabola.. pretty straight foward, right?
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Vertex Form
STRATEGY
Axis of symmetry: A vertical invsible line through the middle of the parabola. It is the x-intercept which is also represented by "h".
Optimal Value (Minimum/ Maximum Value): The highest or lowest point that the parabola reaches. It is the y-intercept which is also represented by "k".
X-intercepts/zeros: The point that the parabola intercepts on the x axis that makes the equation y=0.
Transformations: Vertical translation, reflection, horizontal translation and vertical stretch.
Step Pattern: Use it to determain where the other points go to form the parabola.
Over Up
1 1
2 4
3 9
4 16
5 25
Now, how you use this is you multiply the "up's" by "a" and thats how you get the other points. You start at the corrdinates that give you the vertex then for example you would go over 1 up 1, over 2 up 4.
