Factoring
Factor completely:
x2 + x - 30
(x + 6)(x - 5)
Solve for x by factoring:
x2 - 3x - 18 = 0
x = 6, x = -3
Solve the inequality for x:
4x - 3 > 9
x > 3
What is the yearly multiplier for a football card that increases in value by 2% per year?
1.02
Solve the system of equations:
x = 2y + 4
x + y = 13
(10, 3)
Factor completely:
x2 - 6x + 8
(x - 4)(x - 2)
Solve for x by the Quadratic Formula:
0 = 3x2 + 4x - 7
x = 1 , x = -7/3
Solve the inequality for t:
3(t + 4) < 5
t < -7/3
What is the yearly multiplier for a car that decreases in value by 11% per year?
.89
Write the equation of the line through ( -44, 42) and (-31, 94).
y = 4x + 218
Factor completely:
2x2 - 5x + 4
Not factorable
Solve for x by completing the square:
x2 + 4x + 1 = 0
x = sqrt(3) - 2 which is approximately -.27
x = - sqrt(3) - 2 which is approximately -3.73
When you see an dashed line on an inequality graph, what are the two possibilities for the inequality symbol?
< or >
The cost to rent a DVD has decreased 10% per year over the past several years.
(a) If the current cost is $5, write an exponential equation describing this situation.
(b) What did it cost to rent a DVD 5 years ago?
(a) y = 5(.9)x
(b) $8.47
The hare leaps 500 centimeters every 20 seconds. The tortoise crawls 250 centimeters every 50 seconds, but gets a 1000-centimeter head start. Use any method you know to determine how long it takes the hare to catch up to the tortoise.
50 seconds
Factor completely:
-3x3 + 23x2 -14x
-x(3x - 2)(x - 7)
Solve the quadratic for x using a method of your choice:
9x2 - 8 = -34x
x = 2/9
x = -4
DAILY DOUBLE!
y > (1/2)x - 2
A loaf of bread costs $.60 in 2021. Now (in 2023), a loaf of bread costs $.88. By what percent did the bread increase in cost each year?
21%
Write a system of equations to solve:
Brian was holding an animal fair. He wanted to make sure koalas would come, so he charged kangaroos $5 but koalas only $3. The 45 animals who came paid a total of $175. How many koalas and kangaroos came to the dance?
There were 25 koalas and 20 kangaroos.
Factor completely:
6x3 + 10x2 - 24x
2x(3x - 4)(x + 3)
Solve the quadratic for x using a method of your choice:
15x2 - 165x = -630
No real solutions
Solve the inequality for x:
5x + 4 > 7(x + 3)
x < 17/2
or
x < 8.5
Find the equation of an exponential function in the form y = a(b)x that passes through the points (3, 13.5) and (5, 30.375).
y = 4(1.5)x
Given the quadratic function:
f(x) = (x - 1)2 - 4
(a) State the vertex.
(b) Determine the x-intercepts.
(a) (1, -4)
(b) (3, 0) and (-1, 0)