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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 Notes 20 - Section 4.8
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.
Quadratic Formula A formula that gives the solutions to any quadratic. Given: Formula:
Example 1 Solve for x using the quadratic formula.
Example 2 Solve for x using the quadratic formula.
Example 3 Solve for x using the quadratic formula.
Discriminant The expression is called the discriminant of the equation. It can determine number and type of solutions to a quadratic equation.
Number of Solutions Using the discriminant , if: there are two real solutions there is one real solution there are two imaginary solutions
Example 4 Find the discriminant and determine the number and type of solutions.
Example 5 Find the discriminant and determine the number and type of solutions.
Example 6 Find the discriminant and determine the number and type of solutions.
Example 7 Find the discriminant, tell how many solutions there are, then solve for x.
Class Problem Find the discriminant, determine the number of solutions, then solve for x.
Modeling Quadratic Functions • Falling Objects: • Launched or Thrown Objects:
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 =
Example 8 – Cont. h = 3 ft. t = t v0 = 40 h0 = 4 ft
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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