Quadratics v.s. Piecewise

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Quadratics v.s. Piecewise by Mind Map: Quadratics v.s. Piecewise

1. Quadratic functions

2. comparing to quadratics

2.1. 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.

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

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

3. how to write it

3.1. Piecewise functions are written like this

4. Piecewise Functions

5. Definition

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

6. Examples

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

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

7. Examples

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

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

8. Definition

8.1. 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.

9. 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

10. how to solve

10.1. use the quadratic formula

10.1.1. the formula

10.2. factor

11. Real life examples

11.1. Throwing a ball

11.2. dropping something from a high place

11.3. the cost of things

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

12. comparing to piecewise

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

12.2. quadratics use an easier way to write it out