1. Algebra 1 EOC Summer School Lesson 13: Solve Quadratic Equations

2. Introduction to Solving Quadratic Equations Quadratic Equations can be solved in several ways: – Graphing: by finding the x-intercepts – Factoring: and setting factors equal to zero – Quadratic Formula: gives you both solutions

3. Solve by Graphing What are the solutions of the equation 2x 2 – 16x – 96 = 0? Graph the equation in the calculator. Remember: “=0” is the same thing as “y=“ Adjust the window to see both x-intercepts. x = -4 and x = 12

4. Solve by Factoring What are the solutions to the equation x 2 + x = 6? Make the equation = 0 - 6 x 2 + x – 6 = 0 Find factors of “C” that add or subtract to equal “B” (x+3)(x-2)= 0 Set each factor = 0 and solve. x + 3 = 0x – 2 = 0 - 3 +2 x = 3x = 2

5. Solve by the Quadratic Formula The quadratic formula: To use the quadratic formula, you need to identify the values of “a”, “b” and “c”. Example: f(x) = 2x 2 + 3x – 20 a = 2 b = 2 c = -20

6. Solve by the Quadratic Formula, cont… What are the solutions for the equation 4n 2 – 9 = 23? Make the equation = 0 -23 4n 2 – 32 = 0 Find the values of a, b, and c. a = 4 b = 0 c = -32 Plug these values into the quadratic formula and simplify. = = =

7. Connecting the Vocabulary to Symbols You may be asked to find: SolutionsSolution SetX-interceptsZerosRoots They all mean the same thing! x = -1 and x = 3 {-1, 3} (-1, 0) (3, 0)-1 and 3