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Finding roots graphically

Solving Quadratic. Int 2. Finding roots graphically. Finding roots by factorising. www.mathsrevision.com. Finding roots using formula. Int 2. Starter. www.mathsrevision.com. Graphical Roots. Int 2. Learning Intention. Success Criteria.

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Finding roots graphically

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

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

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

  4. f(x) f(x) x 1 3 x -2 -4 Graphical Roots Int 2 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. www.mathsrevision.com created by Mr. Lafferty

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

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

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

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

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

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

  11. Roots 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 www.mathsrevision.com Note: The a,b in this form are NOT the a,b in the form f(x) ax2 + bx + c created by Mr. Lafferty

  12. Roots Int 2 Examples Factorise using FOIL or St. Andrew’s Cross Factorise 2x2-x-1 = 0 Factorise y2+ 3y = 0 ( 2x+1)(x-1) = 0 y(y + 3) = 0 www.mathsrevision.com either either 2x+1 = 0 x = -0.5 y = 0 or or x-1 = 0 x = 1 y = -3 y + 3 = 0 created by Mr. Lafferty

  13. Roots Int 2 Find the roots of the quadratic equations. Where it cut the x !!!!!! x2 + 7x + 10 = 0 x2 + 6x + 8 = 0 (x + 5)(x + 2) = 0 (x + 4)(x + 2) = 0 x = -2, -5 x = -2, -4 www.mathsrevision.com x2 - 5x – 6 = 0 2x2 - 13x + 15 = 0 (x – 6)(x + 1) = 0 (2x – 3)(x - 5) = 0 x = 6, -1 x = 1.5, 5 created by Mr. Lafferty

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

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

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

  17. Factorise Roots Int 2 When we cannot factorise or solve graphically quadratic equations we need to use the quadratic formula. ax2 + bx + c www.mathsrevision.com created by Mr. Lafferty

  18. Factorise Roots Int 2 Example : Solve x2 + 3x - 3 ax2 + bx + c 1 3 -3 www.mathsrevision.com created by Mr. Lafferty

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

  20. Factorise Roots Use quadratic formula to solve the following : 2x2 + 4x + 1 = 0 x2 + 3x – 2 = 0 x = -1.7, -0.3 x = -3.6, 0.6 3x2 - 3x – 5 = 0 5x2 - 9x + 3 = 0 x = 1.4, 0.4 x = 1.9, -0.9 created by Mr. Lafferty

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

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