1. Write your estimate in your warm-up section.
9/15/17 When you come in…
Write your estimate in your warm-up section.

3. 4-2 Solving Equations by Graphing

4. Root
Zero
Solution
All of these terms mean the x-intercepts of a function, or the x values that make f(x) = 0

5. Possible solutions

6. Example 1
Solve x2 + 6x + 8 = 0 by using the given graph.

8. Steps to Solve by Graphing
Make sure the f(x) or y is isolated
Graph the equation
Look at the x-intercepts to find the solution
Use graph
Use table
Use CALC

9. Solve x2 – 4x = –4 by graphing.
Example 3
Solve x2 – 4x = –4 by graphing.

10. Example 4 Solve –x2 + 4x – 1 = 0 by graphing.
Use the ZERO feature, (2nd [CALC]), to find the zeros of the function.
Enter the left bound for the zero and press [ENTER ].
Enter the right bound and press [ENTER] twice.

11. Locate the zeros in the function 2(x- 3) 2 – 9 = 0
Example 5
Locate the zeros in the function 2(x- 3) 2 – 9 = 0

12. Example 6
The highest bridge in the United States is the Royal Gorge Bridge in Colorado. The deck of the bridge is 1053 feet above the river below. Suppose a marble is dropped over the railing from a height of 3 feet above the bridge deck. How long will it take the marble to reach the surface of the water, assuming there is no air resistance?
Use the formula h(t) = –16t 2 + h0, where t is the time in seconds and h0 is the initial height above the water in feet.

13. Solve by Using a Calculator
Solve 0 = –16t
Graph the related function y = –16t using a graphing calculator. Adjust your window so that the x-intercepts are visible.

15. Write your name with 4 X’s under it
Mr. Van Vleet X X X X

16. 𝑥 2 −11𝑥+19=−5 𝑥 2 −10𝑥+22=−2 7 𝑥 2 −14𝑥=−7 3 𝑥 2 −16𝑥−12=0
Solve each equation
𝑥 2 −11𝑥+19=−5
𝑥 2 −10𝑥+22=−2
7 𝑥 2 −14𝑥=−7
3 𝑥 2 −16𝑥−12=0
7 𝑥 2 +2𝑥=0

17. What is the y-intercept of the following function
𝑓 𝑥 = 𝑥−
𝑦=5 𝑥 2 −7𝑥+2
𝑦=4−2 𝑥 2 +7𝑥

18. How has the graph of 𝑦= 𝑥 2 been shifted to get 𝑦= 𝑥−1 2 +4 ?

19. What is the domain and range of the quadratic function graphed to the right?

21. What are the roots/zeros of the following function?
𝑦=(𝑥+4)(𝑥−7)

22. Homework
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