1. Parabolas in Architecture, Engineering, and Nature
AM 3.1c To Solve Radicals with the Quadratic Formula or Factors
Got ID?
Parabolas in Architecture, Engineering, and Nature

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

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

4. 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?

5. ... 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

6. 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

7. Check: ü
Yes
Check: No

8. 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)

9. Check: ü
Yes No

10. Active Learning Assignment: Solve and Check: (Answers) 1. 2. 3. 4.
Quadratic Test: Tuesday, Oct. 9th
(16)
(3)
(9)
(4, 2)
WOW:
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