1. Solving Equations by Graphing

2. Solving Equations  Solving an equation means finding the value of x if y = 0  There are several ways to solve equations but we are going to focus on graphing, factoring, and the quadratic formula

3. Solving Equations by Graphing IIf you look at a graph, where does y ALWAYS equal 0? TThe x -axis TTo solve an equation by graphing, determine where the graph crosses the x -axis. WWhat names do we have for this point: x -intercept, root, zero, solution

4. Solve: y = | x + 3| - 4  What type of equation?  Absolute value  What does it mean to ‘solve’ it?  Find the value of x when y = 0.  How could we do this by hand?  0 = | x + 3| - 4

5. 0 = | x + 3| - 4 Isolate the absolute value expression. 4 = | x + 3| Split into two equation and solve 4 = x + 3-4 = x + 3 1 = x -7 = x

6. Solve: y = | x + 3| - 4 WWhen we solve by hand, we determine that x = 1, -7 GGraph y = | x + 3| - 4 and determine the zeros. Where does the graph cross the x-axis? x = 1, -7

7. What are the solutions to the equations represented below? x = -3, 0, 4 x = -5, 1 What type of function is this? What are the solutions to this cubic function?What are the solutions to this quadratic function?

8. Find the solution to y = 2 x - 1  What type of equation is it?  Exponential  x = 0

9. Find the roots of y = 3x 2 + x - 2 What type of equation is this?Quadratic What are the roots? x = -1 x = ?

10. Find the roots of y = 3x 2 + x - 2  -1 is obviously a solution, but it is hard to determine the other solution.  The calculator will determine it for you: Graph the function Hit: G-Solv (F5) then Root (F1) (notice it gives the x and y values, what is the y value??)  x =.6666667 is 2 / 3 (use the fraction not the decimal!!!)

11. Find the roots of y = 3 x 2 + x - 2  The roots of y = 3 x 2 + x – 2 are x = -1, 2 / 3

12. Find the roots of y = x 2 + 1  What type of equation is it?  Quadratic  What does it mean to find the ‘roots’?  Find the value of x when y = 0.  How could we do this by hand?  0 = x 2 + 1  -1 = x 2  ± i = x  What does this mean?? Let’s look at the graph.

13. Find the roots of y = x 2 + 1  It doesn’t cross the x =axis. So our solution is…  x = ø

14. Name the type of function and find the zeros using the calculator. Exponential Cubic Square Root x = 1.2619 x = 0, -7 x = 2.5 zeros