Find the vertex of the quadratic function:
y=x^2−4x+3y
(2,−1)
Evaluate the function when x=2
f(x)=x^3−2x^2+3
f(2)=3
A fair six-sided die is rolled once. What is the probability of rolling a 4?
P(4)=1/6
Find the next term in the sequence:
2, 5, 8, 11, …
+3
Next term:14
Find the slope of the line:
y=3x+5
So the slope is:
3
Solve the quadratic equation:
x^2−5x+6=0
x=2orx=3
Solve:
x^3−8=0
x=2
A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
P(blue)=2/10=1/5
Find the 10th term of the arithmetic sequence:
4, 7, 10, 13, …
an=a1+(n−1)d
First term:
a1=4
Common difference:
d=3
Term number:
n=10
So the 10th term is:
31
Write the equation of the line with slope 2 and y-intercept −1
y=2x−1
Solve:
2x2+3x−2=0
x=1/2orx=−2
Factor completely:
x^3−6x^2+11x−6
(x−1)(x−2)(x−3)
A coin is flipped twice. What is the probability of getting two heads?
P(two heads)=1/2×1/2 =1/4=
Find the 6th term of the geometric sequence:
3, 6, 12, 24, …
an=a1r^n−1
First term:
a1=3
Common ratio:
r=2
So the 6th term is:
96
Find the slope of the line passing through:
(2,5)and(6,13)
So the slope is:
2
For the function
y=−x^2+6x−5
find:
vertex=(3,4)
axis of symmetry=x=3
maximum=4
For the function
y=x^3−3x^2−9x+27
find:
x-intercepts:(−3,0),(3,0)
y-intercept:
(0,27)
A card is drawn from a standard deck of 52 cards. Given that the card is a face card, what is the probability that it is a king?
P(king | face card)=4/12 =1/3
Find the sum of the first 20 terms of the arithmetic sequence:
5, 8, 11, 14, …
Sn=n/2(a1+an)
the sum is:
670
For the function
y=−2x+4y
find:
slope:m=−2
y-intercept:(0,4)
x-intercept:
(2,0)
A ball is thrown upward from a height of 5 meters with an initial velocity of 20 m/s. Its height is modeled by
h(t)=−5t^2+20t+5
The ball reaches maximum height after:2 seconds
Maximum height:25 meters
Positive solution:t≈4.24 seconds
The volume of a box is modeled by
V(x)=x(12−2x)(10−2x)
where x is the size of squares cut from each corner.
V(x)=4x3−44x2+120x
Volume:
96 cubic units
domain:0<x<5
A box contains:
Two balls are drawn without replacement.
What is the probability that both balls are blue?
5/33
A sequence is defined recursively by:
a1=2
an=3an−1+1
Find:
First five terms:
2, 7, 22, 67, 202
Final answer:
a6=607
A taxi company charges a $4 starting fee plus $3 per mile traveled.
C(x)=3x+4
Cost:
$34
So the person can travel:
12 miles