s tudy p ages mat170 spring 2009 material for 1 st quiz
TRANSCRIPT
STUDY PAGESMAT170 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 leftf(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 ODD FUNCTION?
WHAT IS MEANT BY AN EVENEVEN 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 a0
4 STEPS FOR FINDING INVERSE FUNCTION:
1. Change the function notation : f(x) f(x) y y
2. Change all the xs to ys and ys to xs
3. Solve for Y
4. Replace y with ff-1-1(x)(x)
DOMAIN QUESTIONS1. Does the function have a denominator? 2. Does the function have a square or even
root? 3. Does the function have a log or ln in it?4. Did the function arise from finding an
inverse?5. Is this a “real world” problem?
Vertical Shifts (outside parentheses)
f(x) + c means the vertex
moves up c
f(x) - c means the vertex
moves down c
Horizontal shifts (inside parentheses)
f(x + c) means the vertex moves left ( ) c
units
f(x - 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)
c f(x) When c > 1 then
stretch
When 0< c < 1 then shrink
Horizontal (inside parentheses)
f(cx) When c > 1 then
shrink
When 0< c < 1 then stretch
WE USE COMPLEX NUMBERSCOMPLEX NUMBERS TO REMOVE NEGATIVE NUMBERS FROM INSIDE RADICALS.
-1 = i and i2 = -1
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 (3-2i)(4+5i)4-5i = (4-5i)(4+5i)