1. created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic www.mathsrevision.com Int 2

2. created by Mr. Lafferty Starter www.mathsrevision.com Int 2

3. created by Mr. Lafferty Learning Intention Success Criteria 1.Use graphs to locate roots of a quadratic equation. 1.To sow how to solve quadratic equations graphically. 2.Solve quadratic equations by finding the roots. www.mathsrevision.com Int 2 Graphical Roots

4. created by Mr. Lafferty www.mathsrevision.com Int 2 Graphical Roots Finding the roots (solve) of a quadratic equation is simply finding where the graph crosses the x – axis ie. f(x) = 0 Example : Find the roots (solve) of the quadratic equations below. 3 -2 f(x) x 1 -4 f(x) x

5. created by Mr. Lafferty www.mathsrevision.com Int 2 Graphical Roots

6. created by Mr. Lafferty www.mathsrevision.com Int 2 Graphical Roots

7. created by Mr. Lafferty www.mathsrevision.com Int 2 Graphical Roots

8. created by Mr. Lafferty Now try MIA Ex 8 Ch14 (page 228) www.mathsrevision.com Int 2 Graphical Roots

9. created by Mr. Lafferty (2,-2) Starter www.mathsrevision.com Int 2 Q.Write down the function represented by the graphs below given that they are of the form and a is either 1 or -1. (1,4) f(x) x (0,-2) (-2,-4) f(x) x y = a(x - b) 2 + c

10. created by Mr. Lafferty Learning Intention Success Criteria 1.To be able to factorise quadratic equations. 1.To explain how to find the roots (solve) quadratic equations by use of factorisation. www.mathsrevision.com Int 2 Roots

11. created by Mr. Lafferty www.mathsrevision.com Int 2 When a number is multiplied by 0 the result is 0. If 7b = 0 then b = 0 If ab = 0 then a = 0 or b = 0 If ( x-a )( x-b ) = 0 then either (x-a) = 0 or (x-b) = 0 Roots Note: The a,b in this form are NOT the a,b in the form f(x) ax 2 + bx + c

12. created by Mr. Lafferty www.mathsrevision.com Int 2 Factorise 2x 2 -x-1 = 0 ( 2x+1)(x-1) = 0 2x+1 = 0 x-1 = 0 x = -0.5 x = 1 or either Factorise y 2 + 3y = 0 y(y + 3) = 0 y = 0 y = -3 or either y + 3 = 0 Examples Factorise using FOIL or St. Andrew’s Cross Roots

13. created by Mr. Lafferty Find the roots of the quadratic equations. Where it cut the x !!!!!! Roots x 2 + 7x + 10 = 0 x 2 - 5x – 6 = 02x 2 - 13x + 15 = 0 x 2 + 6x + 8 = 0 x = 1.5, 5 x = -2, -5 x = -2, -4 x = 6, -1 (x – 6)(x + 1) = 0(2x – 3)(x - 5) = 0 (x + 5)(x + 2) = 0(x + 4)(x + 2) = 0 www.mathsrevision.com Int 2

14. created by Mr. Lafferty Now try MIA Ex9 (page 229) www.mathsrevision.com Int 2 Roots

15. created by Mr. Lafferty Starter www.mathsrevision.com Int 2

16. created by Mr. Lafferty Learning Intention Success Criteria 1.To be able to solve quadratic equations using quadratic formula. 1.To explain how to find the roots (solve) quadratic equations by use quadratic formula. www.mathsrevision.com Int 2 Factorise Roots

17. created by Mr. Lafferty www.mathsrevision.com Int 2 When we cannot factorise or solve graphically quadratic equations we need to use the quadratic formula. Factorise Roots ax 2 + bx + c

18. created by Mr. Lafferty www.mathsrevision.com Int 2 Example : Solve x 2 + 3x - 3 Factorise Roots ax 2 + bx + c 13-3

19. created by Mr. Lafferty www.mathsrevision.com Int 2 Factorise Roots and

20. created by Mr. Lafferty Use quadratic formula to solve the following : Factorise Roots 2x 2 + 4x + 1 = 0 5x 2 - 9x + 3 = 0 3x 2 - 3x – 5 = 0 x 2 + 3x – 2 = 0 x = 1.9, -0.9 x = -1.7, -0.3 x = -3.6, 0.6 x = 1.4, 0.4

21. created by Mr. Lafferty Now try MIA Ex10 (page 232) www.mathsrevision.com Int 2 Factorise Roots