Chapter 7
Since a picture frame
includes a border, the
picture must be
smaller in area than
the entire frame. The
table shows the
relationship between
picture area and frame
length for a particular
line of frames. Is this
an exponential
relationship? Explain.
Side
Length
(in.) 5 6 7 8 9
Picture
Area
(π’π§^π
) 6 12 20 30 42
No; there is no common factor between the picture areas.
Find (x3 β x + 1) β (3x β 1)
x3 β 4x + 2
State the value of the discriminant for the equation. Then determine the number of real solutions of the equation.
x2 + 2x + 1 = 0
0; 1 real solution
Simplify the expression.
β27 + β48 + β12
9β3
Without graphing, estimate the x-intercepts of the graph of f(x) = 7x2 + 9x + 1 to the nearest tenth.
β1.2 and β0.1
Define in your own words: geometric sequence.
Sample answer: A sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ratio.
Factor the polynomial if possible. If the polynomial cannot be factored, write prime.
20q2β 5r2
5(2q + r)(2q β r)
Describe how the graph of the function is related to the graph of f(x)=x^2.
g(x) = (β
3/4) π₯^2 β
1/2
Dilation of f(x)=x^2 compressed vertically, reflected across the x-axis, and translated down 1/2 unit.
State the domain and range of y = β3β(π₯ β 1) + 5.
D = {x | x β₯ 1}; R = {y | y β€ 5}
Find the first term of the geometric sequence with π6 = 256 and π7 = 1024
1/4
Write an equation for the nth term of the geometric sequence 3/100 , 3/10 , 3, β¦. Find the ninth term of this sequence.
a_n = π/πππ Β· 10^(n β 1) ; 3,000,000
Factor the polynomial.
30π₯^3
y + 35π₯^2π¦^2
5x^2 y(6x + 7y)
Solve the equation by using the Quadratic Formula. Round to the nearest tenth if necessary.
π₯^2 + 4x = β1
β3.7, β 0.3
Simplify the expression. β (90)
3β (10)
Solve 8 β 3x = β(4π₯^2 + 20) + 8.
β2
Write a recursive formula for the sequence.
3, 20, 37, 54, β¦
a_1 = 3, a_n = a_n β 1 + 17, n β₯ 2
Solve the equation. 16π¦^2 β 8y = 0
{π, 1/π }
The value of a certain parcel of land
has been increasing in value ever since it was
purchased. The table shows the value of the land
parcel over time.
Year Since Purchasing 0 1 2 3 4
Land Value
(thousands $) $1.05 $2.10 $4.20 $8.40 $16.80
Look for a pattern in the table of values to determine
which model best describes the data. Then write an
equation for the function that models the data.
exponential; y = 1.05 β’2^x
Simplify.
β(2/10)
β5/5
Factor π£^2π₯^2 β 9π₯^2 + π£^2π^2 β 9π^2 completely.
(v + 3)(v β 3)(x^2 + n^2)
Suppose a car that sells for $40,000 depreciates 10% per year. How many years would it take the car to have a value less than $25,000?
5 years
The Combo Lock Company finds that its profit data from 2005 to the present can be modeled by the function y = 4n^2 + 44n + 121, where y is the profit n years since 2005. Which special product does this polynomial demonstrate? Explain.
Sum of squares; it can also be written as (ππ + ππ)^π
Ayzha and Jeremy hold a flashlight so that the light falls on a piece of graph paper in the shape of a parabola. Ayzha and Jeremy sketch the shape of the parabola and find that the equation y = π₯^2 β 3x β 10 matches the shape of the light beam. Determine the zeros of the function.
β2 and 5
Doyleβs log rule estimates the amount of usable lumber in board feet that can be milled from a shipment of logs. It is represented by the equation B = L( (π β4)/4 )^2 , where d is the log diameter in inches and L is the log length in feet. Suppose the truck carries 20 logs, each 25 feet long, and that the shipment yields a total of 6000 board feet of lumber. Estimate the diameter of the logs to the nearest inch. Assume that all the logs have uniform length and diameter.
18 in
The sum of the squares of two consecutive odd integers is 74. Find the two integers.
5 and 7 or β 5 and β7