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4.8 – Use the Quadratic Formula and the Discriminant

4.8 – Use the Quadratic Formula and the Discriminant. 4.8 – Use the Quadratic Formula and the Discriminant. Example 1: Solve x 2 + 3x = 2. 4.8 – Use the Quadratic Formula and the Discriminant. Example 2: Solve 25x 2 - 18x= 12x – 9. 4.8 – Use the Quadratic Formula and the Discriminant.

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4.8 – Use the Quadratic Formula and the Discriminant

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  1. 4.8 – Use the Quadratic Formula and the Discriminant

  2. 4.8 – Use the Quadratic Formula and the Discriminant Example 1: Solve x2 + 3x = 2

  3. 4.8 – Use the Quadratic Formula and the Discriminant Example 2: Solve 25x2 - 18x= 12x – 9

  4. 4.8 – Use the Quadratic Formula and the Discriminant Example 3: Solve -x2 + 4x = 5

  5. 4.8 – Use the Quadratic Formula and the Discriminant In the quadratic formula, the expression b2 - 4ac is called the discriminant of the assosciated equation ax2 + bx + c = 0 You can use the discriminant of a quadratic equation to determine the equation’s number and type of solutions.

  6. 4.8 – Use the Quadratic Formula and the Discriminant

  7. 4.8 – Use the Quadratic Formula and the Discriminant Example 4: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. x2 – 8x + 17 = 0 x2 – 8x + 16 = 0 x2 – 8x + 15 = 0

  8. 4.8 – Use the Quadratic Formula and the Discriminant For an object that is dropped: h = -16t2 + h0 For an object that is launched or thrown: h = -16t2 +v0t+ h0 Initial velocity can be positive, negative, or zero depending on whether the object is launched upward, downward, or parallel to the ground.

  9. 4.8 – Use the Quadratic Formula and the Discriminant Example 5: A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet above the ground and has an initial velocity of 40 feet per second. The juggler catches the ball when it falls back to a height of 3 feet. How long is the ball in the air?

  10. 4.8 – Use the Quadratic Formula and the Discriminant Example 6: A basketball player passes a ball to a teammate. The ball leaves the player’s hand 5 feet above the ground and has an initial velocity of 55 feet per second. The teammate catches the ball when it returns to a height of 5 feet. How long is the ball in the air?

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