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Understanding the Discriminant: Analyzing Solutions of Quadratic Equations

This guide explores the concept of the discriminant in quadratic equations, specifically focusing on how it determines the number of solutions. The discriminant is the expression under the radical in the quadratic formula. If positive, there are two solutions; if zero, one solution exists; and if negative, no real solutions are available. Additionally, we examine how the graph of a function intersects the x-axis, identifying scenarios for zero, one, or two x-intercepts. This resource is essential for mastering quadratic equations.

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Understanding the Discriminant: Analyzing Solutions of Quadratic Equations

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  1. Notes Over 9.7 Using the Discriminant The discriminant is the expression under the radical: If it is Positive: If it is Zero: If it is Negative: Then there are Two Solutions Then there is One Solution Then there is No Solution

  2. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. One Solution

  3. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. Two Solutions

  4. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. No Solution

  5. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. One Solution

  6. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. No Solution

  7. Notes Over 9.7 Finding the Number of Solutions Tell if the equation has two solutions, one solution,orno solution. Two Solutions

  8. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. One x-Intercept

  9. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. Two x-Intercepts

  10. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. Zero x-Intercepts

  11. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. Two x-Intercepts

  12. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. Zero x-Intercepts

  13. Notes Over 9.7 Finding the Number of x-Intercepts Determine whether the graph of the function will intersect the x-axis in zero, one ,ortwo points. One x-Intercepts

  14. Notes Over 9.7

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