Algebra 9.6 The Discriminant.

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Presentation transcript:

Algebra 9.6 The Discriminant

√ The Discriminant + b² - 4ac - b - x = 2a In the quadratic formula, the expression inside the radical is the discriminant. √ + b² - 4ac - b - x = 2a The discriminant can be used to find the number of solutions a quadratic equation has.

Before using Quadratic Formula to solve……. Compute the value of b²- 4ac If the value is: There are 2 solutions POSITIVE There is 1 solution ZERO There are no real solutions NEGATIVE

How b²- 4ac effects the Quadratic Formula POSITIVE numbers have 2 square roots NEGATIVE numbers don’t have square roots ZERO has 1 square root 2 solutions 1 solution no real solutions

Try it with these equations Compute the value of b²- 4ac x²- 3x – 4 = 0 (-3)²- 4(1)(-4) = 9 + 16 = 25 positive, 2 solutions -x²+ 2x – 1 = 0 (2)²- 4(-1)(-1) = 4 - 4 = 0 zero, 1 solution 2x²- 2x + 3 = 0 (-2)²- 4(2)(3) = 4 - 24 = -20 negative, NO solutions

2 solutions 1 solution no solution 2 x-intercepts 1 x-intercept The number of solutions tells you what the related parabola looks like. CROSSER TOUCHER FLOATER/SINKER 2 solutions 1 solution no solution 2 x-intercepts 1 x-intercept no x-intercepts

Homework pg. 544 # 1-20