Introductions to Basic Transformations

Hi my name is Daniel and today we learned about basic functions!!

This function can be expressed as f (x) = x²
 f (x) can also be y.f (x) = y
In class we reviewed some general equations to remember. 
They are the Vertex form and the Standard form
Vertex form is expressed as: y = a(x – h)² + k  and the variables a, h, k each tell you what the function would look like before even graphing.

The sign on "a" tell you whether the function opens up or down. If a < 0 then the function will most likely open down. If a > 0 then the function will most likely open up.
If a increases, the shape narrows, if a decreases, the shape becomes wider.
h and k will be the coordinates of the vertex used to plot the graph.

Standard form is expressed as: y = ax² + bx + c This is a quadratic equation because it is to the power of 2 (x²)

What you need to understand when you are graphing any quadratic is that you are moving, flipping, stretching which are called transformations.
Take the vertex form for example.  y = a(x – h)² + k 
We can move it up or down by adding a constant to our k-value.

k > 0 makes it go up

k < 0 makes it go down

We call k a vertical translation.





We can move the function to the left or right adding a constant to our h-value.

h > 0 makes it go left

h < 0 makes it go right

We call h a horizontal translation.





We can flip it upside down if we multiply the whole function by -1.
  f(x) = -(x²)



We can stretch it in the y-direction by multiplying a constant to our a-value.

a > 1 stretches it

0 < a < 1 compresses it.

 f(x) = 0.35(x²)


That's all you need to know! Hopefully this expanded your knowledge on the principles of transformation.

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