Quadratics
State the vertex
y=5(x+4)2 +20
(-4,20)
Do these coordinates represent a function
(1,2) (2,2)(3,0) (99,0)
Yes
A student is in the process of solving an equation. The original equation and the first step are shown below. Original: 3a + 6 = 2 − 5a + 7 Step one: 3a + 6 = 2 + 7 − 5a Which property did the student use for the first step
Commutative property of addition
When solving p2 + 5 = 8p − 7, Kate wrote p2 + 12 = 8p. The property she used is
1) the associative property
2) the commutative property
3) the distributive property
4) the addition property of equality
4)
y=2x+5
y=-3x-10
x=-3
y=-1
Solve using the quadratic formula
x2-6x+1=0
x=3+radical 32
x=3-radical 32
Which situation can be modeled by a linear function? 1) The population of bacteria triples every day. 2) The value of a cell phone depreciates at a rate of 3.5% each year. 3) An amusement park allows 50 people to enter every 30 minutes. 4) A baseball tournament eliminates half of the teams after each round.
3)
Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min. If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike
1)B
2)5B
3)45-B
Choice 2
Which of the following is not an equation?
(1) 3+1=4+0
(2) 2x2 -2x=8
(3) 2(4x+1)
(4) 1+3=6
3)
A system of equations is given below. x + 2y = 5 2x + y = 4 Which system of equations does not have the same solution?
1) 3x + 6y = 15 2x + y = 4
2) 4x + 8y = 20 2x + y = 4
3) x + 2y = 5 6x + 3y = 12
4) x + 2y = 5 4x + 2y = 12
4)
Write -x2-6-29 in vertex form by completing the square then state the vertex
-1(x+3)2+20
(-3,20)
For a recently released movie, the function y = 119.67(0.61)x models the revenue earned, y, in millions of dollars each week, x, for several weeks after its release. Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5?round to nearest hundredth
17.06
A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to manufacture each radio. If the cost of manufacturing r radios is given by the function c(r) = 5.25r + 125, then the value 5.25 best represents
the amount spent to manufacture each radio
Find the smallest integer that makes −3x + 7 − 5x < 15 true.
0
Solve using Elimination round to the nearest hundredth
5x-2y=10
2x+7y=43
y=6.29
x=4.52
The height, H, in feet, of an object dropped from the top of a building after t seconds is given by H(t) = −16t2 + 144. How many feet did the object fall between one and two seconds after it was dropped? Determine, algebraically, how many seconds it will take for the object to reach the ground.
48 feet
The object will reach the ground in 3 seconds
Given that f(x) = 2x + 1, find g(x) if
g(x) = 2[f(x)]2 − 1
Round to nearest tenth if necessary
x=-.9
x=-.1
If the population of Maine is 100 and grows by approximately 6% a year how large will the population be in 5 years
133 people
The solution to −2(1 − 4x) = 3x + 8 is
1)6/11
2) 2
3) −10/7
4) −2
2) 2
y=x2-6x+3
2x-y=13
solve
x=0
y=3
A square has one side increased in length by two inches and an adjacent side decreased in length by two inches. If the resulting rectangle has an area of 60 square inches, what was the area of the original square?
64 square inches
Frances is selling glasses of lemonade. The function g(t)=t2+4/2 models the number of glasses she has sold, g, after t-hours. What is the average rate at which she is selling lemonade between t = 2 and t = 6 hours.
12 glasses of lemonade per hour
A man and a woman start 380 feet away from each other and walk in a straight line towards each other. If she is walking at a rate of 6 feet per second and he is walking at a rate of 2 feet per second, when will they meet?
47.5 seconds
What is the solution to the equation
3/5(x+4/3) = 1.04?
.4
in an opera theater sections of seating consisting of three rows are being laid out. It is planned so each row will be two more seats then the one before it and 90 people must be seated in each section how many people will be in the third row
32 seats in row 3