Quadratics v.s. Piecewise

1. Quadratic functions

2. Examples

2.1. Shaped in a U or N shape, called a parabola

2.2. The point of quadratics is to show the growth of something

3. Definition

3.1. A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

4. Sources: https://www.mathsisfun.com/sets/functions-piecewise.html https://www.mathsisfun.com/algebra/quadratic-equation-real-world.html http://www.shmoop.com/functions/quadratic-functions-examples.html

5. how to solve

5.1. use the quadratic formula

5.1.1. the formula

5.2. factor

6. Real life examples

6.1. Throwing a ball

6.2. dropping something from a high place

6.3. the cost of things

6.4. driving someplace, i.e going to the store and than coming back

7. comparing to piecewise

7.1. When you graph it, it curves either up or down, unlike piecewise

7.2. quadratics use an easier way to write it out

8. comparing to quadratics

8.1. On a graph, a piecewise function isn't all connected. Like for example on a parabola or even linear function. It usually have two separated lines.

8.2. Unlike quadratics, piecewise use the greater than and less than sign when solving

8.3. When solving a piecewise you are solving for domain and range, not just an x and y

9. how to write it

9.1. Piecewise functions are written like this

10. Piecewise Functions

11. Definition

11.1. a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain

12. Examples

12.1. they use solid and not solid line to show types of functions.

12.2. Piecewise functions use both less and larger than signs (<,>) and the equal sign.