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Quadratic Equations and Solutions in Standard Form

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Understand and solve quadratic equations using the quadratic formula, find discriminants, and analyze solutions. Solve guided practice problems effectively.

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Quadratic Equations and Solutions in Standard Form

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  1. Section 4.8 Notes • Read all of p. 292 until Example 1.

  2. Examples • Solve using the quadratic formula. • 1. x2 + 3x = 2 • 2. 25x2 – 18x = 12x – 9 • 3. -x2 + 4x = 5

  3. 1. x2 + 3x = 2 • Write in standard form. • x2 + 3x – 2 = 0 a = 1 b = 3 c = -2

  4. 2. 25x2 – 18x = 12x – 9 • Write in standard form. • 25x2 − 30x + 9 = 0 a = 25 b = -30 c = 9

  5. 3. -x2 + 4x = 5 • Write in standard form. • -x2 + 4x – 5 = 0 a = -1 b = 4 c = -5 Do Guided Practice #1 to #3. Read p. 294 until Example 4.

  6. Example 4 • Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. • a. x2 – 8x + 17 = 0 • b. x2 – 8x + 16 = 0 • c. x2 – 8x + 15 = 0

  7. a. x2 – 8x + 17 = 0 a = 1 b = -8 c = 17 Two imaginary solutions

  8. b. x2 – 8x + 16 = 0 a = 1 b = -8 c = 16 One real solution

  9. b. x2 – 8x + 15 = 0 a = 1 b = -8 c = 15 Two real solutions Do Guided Practice #4 and #8. Read p. 295 until Example 5.

  10. 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 vertical 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? Round the answer to the nearest thousandth.

  11. h =– 16t2 + v0t + h0 • v0 = 40 feet per second • h0 = 4 feet • h = 3 feet

  12. The is in the air about 2.525 seconds. Do Guided Practice #10. HW: p. 296 (4-48 mult of 4, 68)

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