Linear vs Quadratic Functions

1. **Equation: y=mx+b

2. m: The slope or rate x: The point where the line starts or intersects on the y-axis or the value of the function if x=0.

3. Simply substitute the variables with the values mentioned in the word problem and solve the equation. Then, you can change the m value to get other numbers to place in your graph.

4. Equation: y=mx+b y=10x+400 y=10(12)+400 y=120+400 y=520

5. A small business that sells tires pay their employees $10 an hour. Mary is an employee there. She currently has a balance of $400 in her bank account. Assume she adds all her earnings from the business into her account. If Mary works 12 hours, what will her new balance be?

6. Real World Example:

7. 3. As said in the definition, the graph must be a completely straight line.

8. 2. The variables or terms cannot have exponents.

9. 1. It must have 1 or 2 real variables. If there is another variable in the function, it must be a known value.

10. Identifying a Linear Function:

11. A linear function is any function that graphs to a straight line.

12. Linear Functions:

13. (Video explaining how to identify linear, quadratic, and exponential data sets)

14. By: Emily Belt

15. To find the answer, you must graph the function and find the zeroes. Enter the equation into your calculator and look at the graph. Then complete the procedure to find the zeros. You should have values close to 0 and 2, this means that the rocket was in the air for about 2 seconds.

16. -16x^2 stands for the initial gravitational acceleration in feet, 37x stands for the speed of the ball, and 3 stands for the height when the rocket started it's launch.

17. Equation: f(x)=-16x^2+37x+3

18. Mary launched her model rocket while standing on a hill up into the air. The rocket had a speed of 37 feet per second. The hill she was standing on was 3 feet above the ground. How long was the rocket in the air?

19. Real World Example:

20. Quadratic Functions:

21. 2. Other terms in the function must be x terms and constants. There cannot be any higher exponential values.

22. 1. It must have an x^2 term.(it may have more than one)

23. Identifying a Quadratic Function:

24. A quadratic function is one in the form of f(x)=ax^2+bx+c, where a, b, and c are numbers not equal to zero. A quadratic function graph will always be a curved line called a parabola.