Parabolas in Architecture, Engineering, and Nature

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Presentation transcript:

Parabolas in Architecture, Engineering, and Nature 10-5-18 AM 3.1c To Solve Radicals with the Quadratic Formula or Factors Got ID? Parabolas in Architecture, Engineering, and Nature

Active Learning Assignment Questions: 1a. y = x2 – 6x 7. y = x2 – 2x – 15 9. y = x2 – 2x – 7 10. y = x2 + 4x + 9

Active Learning Assignment Questions: 1. a = b = c = 2. Vertex: 3. x-intercepts: 4. y-intercept: 5. Axis of Symmetry: 6. Other points?

0 = (x – 8)(x – 3) Either x – 8 = 0 or x – 3 = 0 x = 8 or x = 3 LESSON: Find domain restrictions, solve, and check answers: Domain Restrictions? Set x + 1 ≥ 0 Thus: x ≥ -1 (Square both sides) (Express squares) (Multiply, FOIL, or distribute) (Set equal to zero) (Factor or use quadratic formula) 0 = (x – 8)(x – 3) Either x – 8 = 0 or x – 3 = 0 (Set factors equal to zero & solve) x = 8 or x = 3 Are we finished?

... ü ü Find domain restrictions, solve, and check answers: Check x = 8: ... x = 8 or x = 3 ü Now, check, but ALWAYS go back to the original equation! Now, check x = 3: Thus, both x = 8 and x = 3 work! ü

Find domain restrictions, solve, and check answers: Try: → Domain: 2x + 7 ≥ 0 x ≥ -3.5 Which gives: (Zero out one side) Is the domain OK? Let’s check for 1 & - 3 (Factor or use quadratic formula) 6

Check: ü Yes Check: No

Which gives: Check domain, solve, and check for extraneous solutions: Domain: x ≥ 0 Which gives: (Zero out one side) (Now, check) (Factor or use quadratic formula)

Check: ü Yes No

Active Learning Assignment: Solve and Check: (Answers) 1. 2. 3. 4. 1. 2. 3. 4. Quadratic Test: Tuesday, Oct. 9th (16) (3) (9) (4, 2) WOW: Live so that when your children think of fairness, caring, and integrity, they will think of you.