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)