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Quadratic Formula and the Discriminant

Quadratic Formula and the Discriminant. Notes 20 - Section 4.8. Essential Learnings. Students will understand and be able to formulate equations based on quadratic functions.

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Quadratic Formula and the Discriminant

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  1. Quadratic Formula and the Discriminant Notes 20 - Section 4.8

  2. Essential Learnings • Students will understand and be able to formulate equations based on quadratic functions. • Students will be able to solve quadratic equations using the Quadratic Formula and use the discriminant to interpret the nature of the roots of quadratic equations.

  3. Quadratic Formula A formula that gives the solutions to any quadratic. Given: Formula:

  4. Example 1 Solve for x using the quadratic formula.

  5. Example 2 Solve for x using the quadratic formula.

  6. Example 3 Solve for x using the quadratic formula.

  7. Discriminant The expression is called the discriminant of the equation. It can determine number and type of solutions to a quadratic equation.

  8. Number of Solutions Using the discriminant , if: there are two real solutions there is one real solution there are two imaginary solutions

  9. Example 4 Find the discriminant and determine the number and type of solutions.

  10. Example 5 Find the discriminant and determine the number and type of solutions.

  11. Example 6 Find the discriminant and determine the number and type of solutions.

  12. Example 7 Find the discriminant, tell how many solutions there are, then solve for x.

  13. Class Problem Find the discriminant, determine the number of solutions, then solve for x.

  14. Modeling Quadratic Functions • Falling Objects: • Launched or Thrown Objects:

  15. Example 8 A juggler tosses a ball into the air. The ball leaves the hand 4 feet above the ground at an initial velocity of 40 feet per second. The juggler catches the ball when it falls to 3 feet. How long is the ball in the air? h = t = v0 = h0 =

  16. Example 8 – Cont. h = 3 ft. t = t v0 = 40 h0 = 4 ft

  17. Need Extra Help? Don’t get it? BOOST • Blocks 1, 3, 5, 7 in L1100 • Silver and blue days • Math teachers waiting to help you! • One-on-one free tutoring!

  18. Assignment Pages 296 – 298: 6 – 39 (x3), 41, 43, 48, 52 – 54, 68, 70 Complex Numbers Puzzle Due Tuesday/Wednesday Unit Study Guide 2 Due Monday

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