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# Solving by graphing remediation notes

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Solving by graphing remediation notes

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### Solving by graphing remediation notes

1. 1. •Using Graphing
2. 2. Investigating Solutions,X-Intercepts and Factors
3. 3. Solving Quadratics by Graphing
4. 4. Types of Solutions There are 3 possible types of solutions evident from the graph. Look at the number of times the quadratic crosses the x-axis. 2 REAL solutions when the quadratic has 2 different x-intercepts No REAL solution (2 complex roots) when the quadratic has NO x-intercepts (can’t solve by graphing-use completing the square or quadratic formula!!) We will discuss complex later! 1 REALsolution when the quadratic has 1 x- intercept, which is also the vertex (a) 2 real (b) 2 complex (c) 1 real y y 20 10 y 5 16 8 4 12 6 3 8 4 2 4 2 1 x x x −20 −16 −12 −8 −4 4 8 12 16 20 −10 −8 −6 −4 −2 2 4 6 8 10 −5 −4 −3 −2 −1 1 2 3 4 5 -4 -2 -1 -8 -4 -2 -12 -6 -3 -16 -8 -4 -20 -10 -5
5. 5. Examples:Solve each quadratic using graphing. y = 4x² - 20 x  y = 3x² - 5x + 7 +25  Y1=3x²-5x+7 Y1 = 4x²-20x+25  Y2=0 Y2=0  NO intersection 1 intersection (vertex)  No REAL solution x = 5/2 (1 real) 5 4 y  2 complex solutions y 3 20 2 16 12 1 x 8 −5 −4 −3 −2 −1 1 2 3 4 5 4 -1 x -2 −20 −16 −12 −8 −4 4 8 12 16 20 -4 -3 -8 -4 -12 -5 -16 -20
6. 6. You try: Find the real solutions to the quadratic equation. -x² - 4x + 6 = 0  Click HERE to view the solution!
7. 7.  Y1= -x²-4x+6 10 y Y2=0 8 6 2 intersections 4 2 x ≈ -5.16, 1.16 −10 −8 −6 −4 −2 2 4 6 8 10 x -2 (2 real) -4 -6 -8 -10
8. 8. View the following videos for a review of solving by graphing. http://www.phschool.com/atschool/academy123/html/bbhttp://www.purplemath.com/modules/solvqu ad5.htm You may now take the Post Quiz to Complete Module 7.