Download x-2

November 1st
copyright2009merrydavidson
Warm Up
1) Complete the Square to change to
Standard Form.
y
=
2(x
–
f(x) = 2x2 – 8x + 9
2) Find ALL roots using the rational root
theorem, factoring and/or quadratic
formula.
f(x) = x4 + 3x3 – 5x2 - 21x + 22
2)2 + 1
x  1, 2, 3  2i
Polynomial Inequalities
x3 + 3x2 – x – 3 < 0
dashed
Where is the
polynomial less
than 0?
(, 3)  (1,1)
Let’s do this without
having to graph it first.
Polynomial Inequalities
x3 + 3x2 – x – 3 < 0
Step 1: Find the CRITICAL numbers.
Solutions are critical numbers so
solve for x =.
x = + 1, -3
Since it is “<“ and not “<‘;
x  1, 3
place on the x-axis as a hole.
x3 + 3x2 – x – 3 < 0
F
T
-3
T
-1
F
1
Step 2: Test a point on each interval
in the original inequality to see if it is
“true” or “false”.
The solution is the intervals that turn
out TRUE.
(, 3)  (1,1)
Process for solving polynomial
inequalities……
• Pretend it is equal to zero and find zero’s
• Put those on the number line
<, > closed circles
<, > open circles
• Test sections into the ORIGINAL
inequality for T or F
• Write the answer in interval notation for
the true sections
You do this one……
2x3 – 3x2 – 32x > - 48
3
(4, )  (4, )
2
Rational inequalities
x4
0
x2
Find the solution to a rational
inequality algebraically.
Solve rational inequalities (x-2) x  4
(x-2)

0
Step 1:
Rewrite fractions
x2
with factored denominator
Already done
Step 2:
Find domain restrictions. Put this
number on a number line as a “hole”. x  2
-4
x+4=0
2
x = -4
Step 3.
pretend it is = 0 and find the zero’s.
Put this value on the number line as open or closed
circles.
<, > closed circles
<, > open circles
x4
0
x2
Solve rational inequalities
(, 4]  (2, )
T

-4
F
T
2
Step 4: Test intervals using the original inequality.
Step 5.
Write the solution in interval notation.
Process for solving rational
inequalities……
• Find domain restrictions from the denominator
and put a hole on the number line
• Pretend it is equal to zero and find zero’s
• Put those on the number line as open/closed
dots
• Test sections into the ORIGINAL inequality for T
or F
• Write the answer in interval notation for the true
sections
A common mistake is to forget
to do the first step!
2x  7
3
x5
You do this one……
(,5)  [8, )
5
3

x6 x2
You do this one……
(, 14]  (6, )
3x
x

3
x 1 x  4
You do this one……
Quiz next time over….
• Find critical numbers for inequalities
• Solve polynomial and rational inequalities
• Graph a rational function including
intercepts, asymptotes and correct end
behavior
• Function composition
• Evaluating a function for a specific value
HW: WS 4-5