Section 1-8:  Quadratic Models 

Try the quiz at the bottom of the page!
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Quadratic models are used to model certain real-world situations such as:
1)  Values decrease then increase
 
  2)  Values increase and then decrease
 
  3)  Values depending on surface area.
                                           4)  Objects thrown into the air.

Application of curve fitting
Suppose a function has the following points f(0) = 5, f(1) = 10 and f(2) = 19.  Find an equation of the form f(x) = ax2 + bx + c.
5 = 0 + 0 + c means c = 5
10 = a + b + 5 means a + b = 5
19 = 4a + 2b + 5 means 4a + 2b = 14
The last two equations can be solved simultaneously
a + b = 5
2a + b = 7
Subtract the first equation from the second to get:
a = 2
This means that b = 3
Therefore, the equation is 2x2 + 3x + 5 = f(x)

Application to physics!

On to the sample test!! Good luck!
 
Current quizaroo #  1b
 
 
 
1)  Simplify (5 -3i)(2 + 5i)
a)  -5 + 19i
b)  -5 + 31i
c)  25+ 19i
d)  25 + 31i
e)  25 - 19i
 
2)  Write in the form a + bi, the following division problem  1/(3 + 2i)
          a)  (3/5) - (2/5)i 
b)  (3/13) - (2/13)i
c)  (3/5) + (2/5)i
d)  (3/13) + (2/13)i
e)  3 - 2i
 
 
3)  Solve the quadratic formula by any method:  (2x + 1)(4x - 3) = (4x - 3)2
a)  4/3, -1
b)  0, -1
c)  -4/3, 1
d)  -3/4, 1
e)  3/4, 2
 
4)  Name in order the vertex point, axis of symmetry, x-intercepts and y-intercepts for:
                                                            y = x2 + 4x + 3
a)  (-2,-1), x = -2, (-1, 0) and (-3, 0),    (0, 3)
b)  (2, 11), x = 2, (-1, 0) and (-3, 0),     (0, 3)
c)  (-2, 1), x = 2,  (1, 0) and (3, 0),     (0, 3)
d)  (2, 11), x = -2, (1, 0) and (-3, 0),    (0, 3)
e)  (-4, 3), x = 2, (-1, 0) and (-3, 0),      (0, 3)
 
5)  If you drive at x miles per hour and apply your brakes, your stopping distance in feet is approximately f(x) = x + (x2/25).  By how much does your stopping distance increase if you increase your speed from 30 to 40 mi/h?
a) 104 ft
b) 66 ft
c) 38 ft
d) 170 ft
e) doesn't change
 
 
 
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