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) = ax^{2} + bx + c.

Solution:
plug in each point to get three equations

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
2x^{2} + 3x + 5 =
f(x)

Application
to physics!

An
object thrown into the air is modeled by the equation h(t) = -4.9t^{2} + v_{o}t + h_{o} Where v_{o} is
the initial velocity h_{o} is the
initial height above the ground h(t) is the height after
t seconds. A baseball is thrown with
an upward velocity of 14 m/sec from a building 30m high.

1)
Find its height above the ground t seconds later.

Solution:
h(t) = -4.9t^{2}
+ 14 t + 30 Simply substitute in the values.

2)
When will the ball reach its peak?

Solution:
Find its vertex point. x = -b/2a = -14/-9.8
= 140/98 = 10/7 seconds later.

3)
When will the ball hit the ground?

Solution:
This will happen when the height is zero. 0 = -4.9x^{2} + 14t + 30 49t^{2} - 140t -300 = 0 (7x + 10)(7x - 30) =
0 x = -10/7 or x = 30/7 Throw out -10/7 Why? Answer is 30/7
seconds.

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 = x^{2} + 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 +
(x^{2}/25). By how much
does your stopping distance increase if you increase your speed from 30
to 40 mi/h?