Quadratic Functions

General Equation: y=x^2

Quadratic Functions...

  • The Domain is all real numbers.
  • The Range is all real nonnegative numbers.
  • The Function is even.

Graphing Quadratics

  • When graphing quadratics, the graph has an intercept at (0,0)
  • Its decreasing on the interval (-infinity, 0)
  • Its increasing on the interval (0, infinity)
  • Its symmetric with the y-axis.

What are Solutions?

  • The solutions of the Quadratic is when the y value is equal to 0.
  • There are usually two solutions.
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Transformations

a- a makes the parabola stretch or compress.

h- h makes it move left or right.

k- k moves it up and down.

Examples

x^2 + 3

In this equation, the k value is 3. The 3 will make it move up 3.
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(x+3)^2

In this equation, the h value is 3. That means it will move 3 to the left.
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-x^2

In this equation, the a value is negative. This will make it flip.
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Sounds Great Right?

By now I'm sure you understand. There are definitely things in the world I love more than quadratics, but if you enjoy them, feel free to work your little fingers to the bones while solving them!