Transcript Test 1

STUDY PAGES
MAT170 SPRING 2009
Material for 1st Quiz
HOW TO “COMPLETE THE SQUARE”
FOR
f(x) = 3x2 + 27x - 24:
1. Move anything w/o an x to the left
f(x) + 24 = 3x2 + 27x
2. Make the number in front of x2 equal to 1
(f(x) + 24)/3 = x2 + 9x
3.Take the number in front of x, divide by 2 and
then square the result.
(9/2)2
4. Add the result of step 3 to both sides.
(f(x) + 24)/3 + (9/2) 2 = x2 + 9x + (9/2)2
5.Factor the right side.
(f(x) + 24)/3 + 20.25 = [x - (9/2)]2
6. Move everything back to the right and now you
have the standard quadratic function equation.
f(x) = 3[x - (9/2)]2 – 84.75
WHAT IS
MEANT BY AN
EVEN
FUNCTION?
WHAT IS MEANT BY AN ODD FUNCTION?
WHAT IS
THE
STANDARD FORM OF A
QUADRATIC FUNCTION?
The graph of f is a parabola
with vertex at point
(h,k)
if a>0, it opens UPward;
if a<0, it opens DOWNward
IN A STANDARD QUADRATIC FUNCTION, WHAT ARE
THE FORMULAS FOR THE POINTS ON THE
VERTEX (H, K) ?
WHAT IS
THE QUADRATIC
FORMULA?
For standard quadratic equations:
ax2 + bx + c = 0 am0
4 STEPS FOR FINDING INVERSE FUNCTION:

1. Change the function notation : f(x)  y

2. Change all the xs to ys and ys to xs

3. Solve for Y

4. Replace y with f-1(x)
DOMAIN QUESTIONS
1.
2.
3.
4.
5.
Does the function have a denominator?
Does the function have a square or even
root?
Does the function have a log or ln in it?
Did the function arise from finding an
inverse?
Is this a “real world” problem?
Vertical Shifts
(outside parentheses)
f(x) + c
Horizontal shifts
(inside parentheses)
f(x + c)
means the vertex moves
up c
means the vertex
moves left ( ) c units
f(x) - c
f(x - c)
means the vertex
moves down c
means the vertex
moves right ( ) c units
(outside parentheses)
Will reflect around the
X axis
(inside parentheses)
Will reflect around the Y axis
Vertical

(outside parentheses)
Horizontal

(inside parentheses)
c f(x)


When c > 1 then
stretch
When 0< c < 1 then
shrink
f(cx)


When c > 1 then
shrink
When 0< c < 1 then
stretch
WE USE COMPLEX NUMBERS TO
REMOVE
NEGATIVE NUMBERS FROM INSIDE RADICALS.
p-1 = i
and
i = -1
2
HOW DO
YOU FIGURE THE EXPONENTS OF
i?
If it divides evenly by 4, then the answer is 1.
The repeating pattern is:
-1,
-i, 1, i
i2 =-1 i3=-i i4=1 i5=i
WHAT IS
A COMPLEX CONJUGATE?
HOW DO
YOU DIVIDE BY A COMPLEX NUMBER?
3-2i
4-5i
=
(3-2i)(4+5i)
(4-5i)(4+5i)