Quadratic Functions
Consider the pattern: 2, 4, 8,...
Which type of model, linear or exponential, should be used to determine the next numbers in the pattern? Explain why.
What is exponential, because there is not a constant rate of change.
Determine the solution the the equation below:
4(x-7)=.3(x+2)+2.11
What is x=8.3
Determine the zeros of f(x)=x2-4x+3 algebraically.
What is x=3 and x=1
State whether 7-sqrt(2) is rational or irrational. Explain your answer.
What is Irrational because the sum of an irrational and rational number is always irrational.
Does not repeat or terminate.
What is the equation of the axis of symmetry for the given function: f(x)=3x2+12x+11
What is x=-2
Write an explicit formula for a geometric sequence with an initial term of 20 and a common ratio of .25.
What is f(x)=20(.25)n-1
Determine if the point (-3,2) is a solution to the following systems below:
2y<-12x+4
y<-6x+4
What is Yes, because when substituted into the systems, they result in true statements, OR Yes, because is lies in the solution set (double shaded area).
What are the solutions to the equation 3(x-4)2=27
What is x=1, and x=7
Subtract -2x2+4x+2 from 3x2+4x-8
What is 5x2-10
Determine the zeros of the following function f(x)=3x2+10x-8
What is x=(-2/3) and x=-4
Anne invested $1000 in an account with 1.3% annual interest rate. She made no deposits or withdraws on the account for 2 years. If interest was compounded annually, write an equation that represents the balance in the account after the second year.
What is A=1000(1+.13)2
Using the formula for volume of a cone, express r in terms of V, h and pi.
What is the sqrt(3v/pih)
Solve the equation x2-6x=15 by completing the square. Express your answer in simplest radical form.
What is x=3+2sqrt(6) and x=3-2sqrt(6)
Determine the number of solutions to the systems of equations below:
y=2x+8
3(-2x+y)=12
What is no solutions.
The equation of a quadratic in vertex form with a leading coefficient of -1/2, and a vertex at (15,25) is...
What is f(x)=-(1/2)(x-15)2+25
The results of a linear regression are shown below
y=ax+b
a=-1.54
b=139.01
r=-.89
r2=.80
Use the correlation coefficient to determine the relationship between x and y
What is strong negative correlation (r=-.89)
For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.
What is
18j+32w=19.92
14j+26w=15.76
The zeros of the function f(x)=2x3+12x-10x2 are:
What is {0, 2, 3}
Jim is a furniture salesman. His weekly pay is $300 plus 3.5% of his total sales for the week. Jim sells x dollars' worth of furniture during the week. Write a function, p(x), which can be used to determine his pay for the week.
Use this function to determine Jim's pay to the nearest cent for a week when his sales total is $8250.
What is p(x)=.035x+3000
p(8250)=$588.75
An air force pilot is flying at a crusing altitide of 9000 feet and is forced to eject from her aircraft. The function h(t)=-16t2+128t+9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft. Determine and state the vertex of h(t). Explain what is means in the context of the problem.
What is (4, 9256) at 4 seconds after she is ejected, she is at a height of 9,256 ft above the ground.
Given the function f(n) defined by the following:
f(1)=2
f(n)=-5f(n-1)+2
Determine the first 4 elements of the range (first 4 terms)
What is 2, -8, 42, -208
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1 50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles. Write a system of inequalities that can be used to represent this situation.
If the club sells 144 cans of lemonade, what is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer.
What is
2L+1.5W>=500
L+W<=360
142 bottles
Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.
What is 7 and 8.
Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option(s) will enable him to reach his goal. Justify your answer.
What is A(x)=100x+10
B(x)=10(2)x
Either option will enable Michael to reach his goal