1. Solving Quadratic Equations By Graphing By: Brielle Woods

2. Quadratic Equations A quadratic equation is a polynomial equation of the second degree. The form for a quadratic equation is: ax2 + bx + c = 0. The solutions of a quadratic equation are called roots.

3. Two Roots Example x 2 + 2x +3 = 0 Original equation x 2 + 2x +3 = 0 Original equation Axis of symmetry is or Axis of symmetry is or Axis of symmetry Axis of symmetry (-1) 2 + 2(-1) + 3 = 0 Plug in -1 for “x” (-1) 2 + 2(-1) + 3 = 0 Plug in -1 for “x” ( -1, 2) Coordinates of the Vertex ( -1, 2) Coordinates of the Vertex

4. Two Roots Example (continued) Make a table of other points to sketch the graph. Make a table of other points to sketch the graph. xf(x) -232 03 16 211

5. Two Roots Example (continued) Graph Graph

6. z 2 + 3z = 18 Original Problem z 2 + 3z = 18 Original Problem Subtract 18 from both sides of the equation. Subtract 18 from both sides of the equation. z 2 + 3z (– 18) = 9 (-18) z 2 + 3z (– 18) = 9 (-18) z 2 + 3z – 18 = 0 z 2 + 3z – 18 = 0 Factor Factor (z - 3)(z + 6) = 0 (z - 3)(z + 6) = 0 A Double Root Example

7. A Double Root Example (Continued) Zero Product Property Zero Product Property (z - 3) = 0 (z - 3) = 0 Add 3 to both sides of the equation. Add 3 to both sides of the equation. z – 3 (+3) = 0 (+3) z – 3 (+3) = 0 (+3) z = 3 z = 3 (z + 6) = 0 (z + 6) = 0 Subtract 6 from both sides of the equation. Subtract 6 from both sides of the equation. z + 6 (-6) = 0 (-6) z + 6 (-6) = 0 (-6) z = -6 z = -6 The roots are z = -6 and z = 3 The roots are z = -6 and z = 3

8. Practice Problems Solve each equation by graphing. Solve each equation by graphing. g 2 + 14g + 40 = 0 g 2 + 14g + 40 = 0 t 2 + 5t = 25 t 2 + 5t = 25 s 2 + 16s + 20 = 0 s 2 + 16s + 20 = 0 a 2 + 10a = 30 a 2 + 10a = 30 b 2 + 24b + 40 = 0 b 2 + 24b + 40 = 0 x 2 + 15x = 35 x 2 + 15x = 35 z 2 + 26z + 30 = 0 w 2 + 20w =40 y 2 + y +12 = 0 r 2 + r = 25 q 2 + q + 2 = 0 p 2 + p = 18

9. Graphic Organizer Solving Quadratic Equations By Graphing 2. Find the Axis of symmetry 3. If the equation equals to zero factor it out 4. If there is a number on the other side of the equal side add or subtract that number to both sides of the equation then factor 5. Make a table with other points to make a correct graph 6. Use the points to graph 1. Find a,b,c

10. Answer key 1.2. 3.

11. Answer key 4.5. 6.

12. Answer key 7. 8. 9.

13. Answer key 10. 11. 12.

14. Web - Resources Game: http://www.coolmath.com/calculators/quadratic. htm Game: http://www.coolmath.com/calculators/quadratic. htm http://www.coolmath.com/calculators/quadratic. htm http://www.coolmath.com/calculators/quadratic. htm Educational: http://www.algebra.com/algebra/homework/qua dratic/ Educational: http://www.algebra.com/algebra/homework/qua dratic/ http://www.algebra.com/algebra/homework/qua dratic/ http://www.algebra.com/algebra/homework/qua dratic/ Assessment: http://www2.wnyric.org/1055104913545267/lib/10 55104913545267/math_student_handouts_hs.pdf Assessment: http://www2.wnyric.org/1055104913545267/lib/10 55104913545267/math_student_handouts_hs.pdf http://www2.wnyric.org/1055104913545267/lib/10 55104913545267/math_student_handouts_hs.pdf http://www2.wnyric.org/1055104913545267/lib/10 55104913545267/math_student_handouts_hs.pdf