Miscellaneous Unit 2
(3-4i)+(2+9i) = ?
5+5i
When f(x)>0, is the graph of f(x) above, below, or on the x-axis?
above!
What is the vertex?
f(x) = 4(x-3)+5
(3,5)
What is (x-4i)(x+4i)
x2+16
Name 5 students in the other Precalculus (Honors) class.
Is (x+3) a factor of x2+7x+12?
yar
What is the maximum number of real zeros the function f(x) = 5x4+6x3-11 has?
4
Find the x-intercept and y-intercepts of
f(x)= (x2+6x+9)/(x-5)
x-intercepts: (-3,0)
y-intercepts: (0,-9/5)
If -2i is a zero of a function, what number must also be a zero?
2i (the complex conjugate)
When is our last day of school?
June 11th!
Is 3 a complex number
Yesssss! It is equal to 3+0i
Find the remainder when you divide x3-8x-2 by x-4
remainder: 30
Write the following equation in vertex form:
f(x) = 2x2-4x+5
f(x) = 2(x-1)2+3
If a polynomial has degree=5 and three real zeros, how many imaginary zeros must it have?
2
What is my first name?
Kathryn
4i3 = ?
-4i
Divide the polynomials:
x3-4x2+2x-3
__________
x+2
x2 - 6x + 14 - 31/(x+2)
Find the HAs and VAs:
f(x)= (3x-2)/(2x2-8)
HA: y=0
VA: x=-2 and x=2
Find the linear factorization of f(x) = x3 + 49x. You may use a calculator but it won't help much.
x(x+7i)(x-7i)
Name one of my grandchildren?
Answers will vary
Write the function as a product of irreducible quadratic and linear factors:
h(x) = x3-6x2+4x-24
h(x) = (x2+4)(x-6)
(x2+4x+4)(x2+9)<0
No real solutions
Solve the following rational equation:
1/x2 = (3+x)/x2 + 5/x
x = -1/3
Determine where the following function is zero, negative, possible, and undefined (imaginary)
f(x)=(x-2)*sqrt(x+6)
f(x)=0 at x=-6,2
f(x)>0 on (2,infinity)
f(x)<0 on (-6,2)
f(x) is undefined on (-infinity,-6)
Make the number 13 with four 4s. You have 2 minutes, GO!
One solution: (44/4) + sqrt(4) = 13