Solve the problem.
A farmer has 1400 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that only three sides need to be fenced. Estimate the largest area that can be fenced.
245,000 ft^2
Solve the problem.
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?
1.5 ft
Solve the problem.
Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 3x^2 - 162x + 84 where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?
27 watches
Solve the problem.
John owns a hot dog stand. He has found that his profit is represented by the equation P(x) = -x^2 + 62x + 72 with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?
31 hot dogs
Solve the problem.
John owns a hotdog stand. His profit is represented by the equation P(x) = -x^2 + 12x + 45 with P being profits and x the number of hotdogs sold. What is the most he can earn?
$81
Solve the problem.
The polynomial function I(t) = -0.1t^2 + 1.9t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?
9.5 year
Solve the problem.
Your company uses the quadratic model y = -11x^2 + 350x to represent how many units (y) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 30?
600 units
Solve the problem.
x and y are two positive numbers and y is three greater than x. The product of the numbers is 154. Find the smaller number, x.
11
Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x^2 should be positive or negative.
The height of a b
Quadratic; negative
Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x^2 should be positive or negative.
The height of a b
Quadratic; negative
Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x^2 should be positive or negative.
The amount of wat
Linear; positive
Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x^2 should be positive or negative.
The amount of sal
Linear; positive
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = (x - 3)^2 - 4
Domain: (-?, ?); Range: [-4, ?)
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = (x - 1)^2 - 4
(-1, 0) and (3, 0)
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = -2(x - 1)^2 + 4
Domain: (-?, ?); Range: (-?, 4]
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = -2(x - 1)^2 + 5
x = 1
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = -2 (x - 5)^2 + 3
(5, 3)
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = -2(x - 5)^2 + 2
x = 5
Use the equation and the corresponding graph for the quadratic function to find what is requested.
f(x) = -2 (x - 5)^2 + 4
(5, 4)