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Find the x coordinate using -b/2a, then find the y coordinate.

Learn to solve quadratic equations using the quadratic formula. Practice with examples and step-by-step solutions provided.

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Find the x coordinate using -b/2a, then find the y coordinate.

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  1. Find the x coordinate using -b/2a, then find the y coordinate. • 1.) y = x2 + 4x - 2 • 2.)y = 2x2 - 4x - 4

  2. 1.)y = x2 + 4x - 2 • x = - (4)/2(1) = -2 • y = x2 + 4x - 2 • y = (-2)2 + 4(-2) - 2 • y = 4 - 8 - 2 • y = -6 Vertex = (-2,-6)

  3. 2.)y = 2x2 - 4x - 4 • x = - (-4)/2(2) = 1 • y = 2x2 - 4x - 4 • y = 2(1)2 - 4(1) - 4 • y = 2 - 4 - 4 • y = -6 Vertex = (1,-6)

  4. Today’s Objective • To be able to solve a quadratic equation by using the quadratic formula.

  5. Solving Equations with a radical Solve for x Review • x2 = 81 • x = 81 • x =  9

  6. Solving Equations with a radical Solve for x Review • x2 = 5 • x = 5 • x =  5

  7. The Quadratic Formula • For equations of the form • ax2 + bx + c = 0 • x = -b b2 - 4ac 2a

  8. The Quadratic Formula • Minus b, plus or minus the square root of b2 minus 4ac divided by 2a

  9. The Quadratic Formula • x = -b b2 - 4ac 2a

  10. The Quadratic Formula y = ax2 +bx + c x2 -3x -18 = 0 x = -b b2 - 4ac 2a x = --3 (-3)2 - 4•1•(-18) 2•1

  11. The Quadratic Formula x = --3 (-3)2 - 4•1•(-18) 2•1 x = 3 + 9 + 72=3+ 81 2 2 x =3 + 9 = 6 2 x =3 - 9 = -3 2

  12. So The Solution is::: • x2 -3x -18 = 0 • x = 6 and -3

  13. The Quadratic Formula y = ax2 +bx + c x2 - 9x + 18=0 x = -b b2 - 4ac 2a x = --9 (-9)2 - 4•1•18 2•1

  14. The Quadratic Formula x = --9 (-9)2 - 4•1•18 2•1 x = 9 + 81 - 72=9+ 9 2 2 x =9 + 3 = 6 2 x =9 - 3 = 3 2

  15. So The Solution is::: • x2 -9x +18 = 0 • x = 6 and 3

  16. Now You TryFirst replace a,b,c in the formula • x2 +3x -18 = 0 • x = -b b2 - 4ac 2a

  17. Now You TryFirst replace a,b,c in the formula • x2 +3x -18 = 0 • x = -3 32 - 4•1•(-18) 2•1

  18. Now solve the formula • x = -3 32 - 4•1•(-18) 2•1 • x = -3 9 + 72 2

  19. Now solve the formula • x = -3 81 2 • x = -3 9 2 x = 3, -6

  20. Classwork • Worksheet 9.4 • Extra Practice (1-6) • Homework page 475 (7-17)

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