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The Quadratic Equation

The Quadratic Equation. The Quadratic Equation. We use it when there are no whole number factors A good clue as to when to use is it is when the question asks for the answer in decimal or square root form The first step is to arrange the equation in the form of a x 2 + bx + c = 0. a = 2.

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The Quadratic Equation

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  1. The Quadratic Equation

  2. The Quadratic Equation • We use it when there are no whole number factors • A good clue as to when to use is it is when the question asks for the answer in decimal or square root form • The first step is to arrange the equation in the form of ax2+ bx + c = 0

  3. a = 2 b = 3 y = 2x2 + 3x +6 c = 6

  4. a = 5 b = 2 y = 5x2 + 2x +1 c = 1

  5. a = 1 b = -6 y = x2 - 6x +11 c = 11

  6. a = 4 b = 1 y = 4x2 + x- 7 c = - 7

  7. a = 2 b = 1 y = 2x2 + x c = 0

  8. x2 + 4x -2=0 Start with the quadratic equation Put in our values for a, b and c Tidy up You need to do this twice, once adding and once taking away x = -4.4 (1dp) and x = 0.4 (1dp) and

  9. 2x2 + 4x +2=0 Start with the quadratic equation Put in our values for a, b and c Tidy up The square root of zero is zero and x = -2 They both give

  10. 2x2 + 3x +6=0 Start with the quadratic equation Put in our values for a, b and c Tidy up We can’t find the square roots of a negative so there is no solution

  11. x2 + 4x -2=0 has 2 solutions 2x2 + 4x + 4=0 has 1 solution 2x2 + 3x +6=0 has no solutions

  12. The quadratic equation • For each of these equations, what is a, b and c? (the first one has been done for you) • 2x2+4x -3 =0 a=2 b=4 c=-3 • 6x2+x - 10=0 • x2-4x -5=0 • 2x2-10x + 7=0 • 0.5x2+8x + 2=0 • Use your answers from question one to find the possible values for x. • Rearrange these equations to the form ax2 + bx + c =0, then solve with the quadratic equation: • 2x2+ 9x -2 =10 • 4x + 5x2 - 10=2 • x2 + 5x -3=x • 2x2-10x - 2= x2 • 3x2 + 6 + 2x =8 + 7x

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