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Mastering Quadratic Equations: Formulas, Solutions, and Discriminant

Review, simplify, and solve quadratic equations using the Quadratic Formula and Discriminant. Learn methods to determine solutions and types of solutions, including factoring and square root properties. Practice writing quadratic equations from given solutions and summarize key concepts.

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Mastering Quadratic Equations: Formulas, Solutions, and Discriminant

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  1. Review: Simplify

  2. Review Solve the equation 5) 6) 7)

  3. Chapter 8 section 2 The Quadratic Formula

  4. Quadratic Equation • Standard form: ax2 + bx + c = 0 with a ≠ 0

  5. Determine the ‘a’, ‘b’, ‘c’ 1) 2x2 – 6x + 7 = 0 2) 3) 4)

  6. Quadratic Formula • Solution of a quadratic equation in standard form ax2 + bx + c = 0 with a ≠ 0 x =

  7. Use the quadratic formula and solve 5) 6) 7)

  8. The Discriminant • b2 – 4ac • Greater than zero: Two unequal real solution • Equal to zero: One solution • Less than zero: Two imaginary solutions.

  9. Determine the number and type of solutions. 7) 8)

  10. Ways to Solve Quadratic Equations • Factor and use the zero-product property: ax2 + bx + c = 0 • Solve for x2 and use the square root property: ax2 + c = 0 • Use the square root property: x2 = c • Use the quadratic formula: ax2 + bx + c = 0

  11. Solve • 3x2 +5x – 2 = 0 • 4x2 – 7 = 0 • (x + 4)2 = 5 • x2 – 2x – 6 = 0

  12. Writing Quadratic Equations If solutions are -5 and 5, what is the equation? Solutions are: x = 5 and x = - 5 x – 5 = 0 or x = - 5 (x – 5)(x + 5) = 0

  13. Write the quadratic equation in standard form 9) 10)

  14. Summary • Quadratic Formula • Discriminant • Ways to Solve Quadratic Equations • Equation from Solutions

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