Quadratic Functions
Find the vertex and the axis of symmetry:
-2x^2-4x-3
(-1,-1)
x=-1
Determine the end behavior:
f(x)=3-8x^3+2x-10x^5
As x->-oo, f(x)->oo
As x->oo, f(x)->-oo
Determine the horizontal asymptote:
y=(9-x^2)/(x+1)
Does not have a HA.
Simplify:
16^(3/4)
8
Evaluate:
log_2(1/16)
-4
If the Old Mill Brewpub offers 5 different hamburgers, 6 different sides, and 4 different drinks, how many different meals can be ordered from this menu?
120
Is the sequence arithmetic, geometric, or neither? State how you know.
-16, -8, -4, -1,...
Geometric, because there is a common ratio of 1/4 .
Solve:
x ^2 + 8 x + 12 >= 0
(- oo, -6] uu [-2, oo)
Divide using long division or synthetic division:
(3x^3-8x^2-51x-55)/(x-6)
3x^2+10x+9 with a remainder of -1
Determine the LCD:
(x-y)/(6xy^2)-(6x)/(4y^3)
12xy^3
Simplify:
root(3)((250x^5y^8)/(2x)
5xy^2root(3)(xy^2)
Facebook is the most popular social media platform with a current user base of close to 3 billion. If it increases its user base by about 2.5% per month, write a function to represent its growth in users measured in billions.
f(t)=3*1.025^t
How many different ways can Mrs. McFarland arrange her 6 racing medals on a wall?
720
Find the explicit formula for the following arithmetic sequence.
51,48,45,42,39,...
a_n=51-3(n-1)
or
a_n=-3n+54
Find the value that will complete the square:
x^2-7x + " = 9 "
49/4
Factor completely:
x^4-x^2-2
(x^2+1)(x^2-2)
Solve for x:
1/(x+4)=(x+1)/(x+2)+1/(x+2)
x=-3
Given: f(x)=-x^2+4x and g(x)=1/2x-5 , find (g@f)(x) and find the domain.
(g@f)(x)=-1/2x^2+2x-5
Domain: (-oo, oo)
Determine the y- intercept of:
y=-5*(1/2)^(x-1)-1
(0,-11)
Your family of 6 is about to play a board game that involves teams of 2. How many teams can be created?
15
Solve.
8ln4v=8
e/4
How many solutions will the following system have?
{(2x,+,y,=,2),(y,=,(x-1)^2,+,1):}
One solution
Given (x-5) is a factor of x^3-3x^2+2x-60 , find all the zeros.
{5, -1+-isqrt(11)}
Find the x- intercept:
y-8=1/(x+3
(-25/8,0)
Find the inverse of:
f(x)=(3x-1)/5
g(x)=(5x+1)/3
Solve:
2^(x+2)+4=46
x=log_2(42)-2
x=(log42)/log2-2
x~~3.3923
Find the probability of:
P(ace or a diamond)
4/52+13/52-1/52=4/13
Find the discriminant and state the number and type of solutions.
y=-9x^2+6x-1
D=0 and one real solution
Factor completely!
x^3+5x^2-x-5
(x+5)(x-1)(x+1)
Use the Binomial Theorem to expand the expression:
(x+y)^3
x^3+3x^2y+3xy^2+y^3
Determine the RPOD:
f(x)=(-x^2+x+2)/(x^2-5x+6)
(2,3)
Solve:
sqrt(7-x)=-1+sqrt(10-x)
x=6
Solve:
logx+log(x+48)=2
x=2
Extraneous: x!=-50
Three bad eggs are put into a carton with 9 good eggs. If 2 eggs are selected at random without replacement, find the probability of the following event. Give your answer rounded to the nearest whole percent.
-The first egg is good, the second egg is bad.
20%
Identify all the transformation.
y=-1/2*e^(-1/2(x+1))+10
Reflection across the x- axis.
Vertical compression by a factor of
1/2 .
Reflection across the y- axis.
Horizontal stretch by a factor of 2 .
Shift left 1 and shift up 10 .