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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Explain how to solve a quadratic equation graphi- cally. How many solutions are possible? Why?
In one study the efficiency of photosynthesis in an Antarctic species of grass was investigated. The table lists results for various tem- peratures. The temperature x is in degrees Celsius and the
The table at the top of the next column shows approximate global sales in millions of cars with self-driving features, such as remote valet assistant and autopilot with lane-changing.(a) Discuss the
The table lists the velocity and distance traveled by a falling object for various elapsed times.(a) Make a scatterplot of the ordered pairs determined by (time, velocity) and (time, distance) in the
Projections for Instagram's revenue in billions of dollars are shown in the following table from 2015 to 2020.(a) Find a quadratic function f that models this data. Support your result by graphing
The table shows the height of a projectile that is shot into the air.(a) Uses (t) = -16t2 + v0t + h0 to model the data. (b) After how long did the projectile strike the ground? t (seconds) s
The price of one airline ticket is $250. For each additional ticket sold to a group, the price of every ticket is reduced by $2. For example, 2 tickets cost 2 · 248= $496 and 3 tickets cost 3 · 246
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
The following table shows Facebook's monthly active users in millions who use a mobile only platform.(a) Discuss the general trend in users during this time period. (b) Would a linear function model
Use least-squares regression to find a quadratic function f that models the data given in the table. Estimate f(3.5) to the nearest hundredth. x 0 f(x) -1 2 16 4 57 6 124
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
A window comprises a square with sides of length x and a semicircle with diameter x, as shown in the figure. If the total area of the window is 463 square inches, estimate the value of x to the
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
Use least-squares regression to find a quadratic function f that models the data given in the table. Estimate f(3.5) to the nearest hundredth. 10 20 30 f(x) 4.2 24.3 84.1 4 40 184
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
A frame for a picture is 2 inches wide. The picture inside the frame is 4 inches longer than it is wide. See the figure. If the area of the picture is 320 square inches, find the outside dimensions
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United
The heart rate of an athlete while weight training is recorded for 4 minutes. The table lists the heart rate after x minutes.(a) Explain why the data are not linear. (b) Find a quadratic function f
The table shows the heart rate of an athlete upon stopping a moderate activity.(a) Model the data with H(t) = a(t = h)2 + k. What is the domain of H? (b) Approximate the athlete's heart rate for t =
Explain how to find the coordinates of the vertex on the graph of a parabola. Then give an example.
Explain the effect that the constant a has on the graph of y = ax2. Be sure to consider a < 0 and a > 0.
The following table shows approx- imate global sales of personal computers in millions of units for selected years.(a) Discuss the general trend in sales during this time period. (b) Would a linear
The table lists the number of iPhones sold in millions in the first 5 years on the market. Find a quadratic function f that models the data. Year 1 2 3 4 5 1 20 50 100 180 Units sold
A company charges $20 to make one monogrammed shirt but reduces this cost by $0.10 per shirt for each additional shirt ordered up to 100 shirts. If the cost of an order is $989, how many shirts were
A rectangular pen for a pet is under construction using 100 feet of fence. (a) Find the dimensions that give an area of 576 square feet. (b) Find the dimensions that give maximum area.
Explain why the vertex is important when you are trying to find either the maximum y-value or the minimum y-value on the graph of a quadratic function.
Repeat Exercise 133 for a suspension bridge that has 100-foot towers, a length of 200 feet, and a cable that comes within 15 feet of the road at the center of the bridge.Data from Exercise 133If the
How do the values of a, h, and k affect the graph of f(x) = a (x - h)2 + k?
Braking distance for cars on level pavement can be approximated by D(x) = x2/30k The input x is the car's velocity in miles per hour and the output D(x) is the braking distance in feet. The positive
Find f(x) = a(x - h)2 + k so that f models the data exactly. x-2 2 A -1 0 2 1 -4-14 2
Find f(x) = a(x - h)2 + k so that f models the data exactly. x-1 y 5 0 1 2
A cylindrical aluminum can is being constructed to have a height h of 4 inches. If the can is to have a volume of 28 cubic inches, approximate its radius r.
If the weight of the deck and the cars is significantly greater than weight of the cables supporting a suspension bridge, such as the Golden Gate Bridge, then the shape of these cables can be modeled
A box is being constructed by cutting 4-inch squares from the corners of a rectangular sheet of metal that is 10 inches longer than it is wide. If the box is to have a volume of 476 cubic inches,
A box is being constructed by cutting 2-inch squares from the corners of a square sheet of metal. If the box is to have a volume of 1058 cubic inches, find the dimensions of the metal sheet.
The width of a rectangular computer screen is 2 inches more than its height. If the area of the screen is 143 square inches, determine its dimensions symbolically, graphically, and numerically. Do
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid
From 1984 to 1994 the cumulative number of AIDS cases can be modeled by the equation C(x) = 3034x2 + 14,018x + 6400, where x represents years after 1984. Estimate the year when 200,000 AIDS cases had
The number of unique monthly visitors in millions to Facebook can be approximated by V(x) = 16x2 + 7x + 32, where x is the number of years after 2008. Estimate the year when Facebook averaged 55
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid
A baseball is thrown downward with an initial velocity of 30 feet per second from a stadium seat that is 80 feet above the ground. Estimate to the nearest tenth of a second how long it takes for the
A baseball is dropped from a stadium seat that is 75 feet above the ground. Its heights in feet after seconds is given by s(t) = 75 - 16t2. Estimate to the nearest tenth of a second how long it takes
A larger square has sides that are 4 inches longer than a smaller square. The sum of the areas of the two squares is 80 square inches. Find the dimensions of each square.
Two rectangles both have lengths that are double their widths. The larger rectangle has a width that is 2 inches greater than the width of the smaller rectangle. If the sum of the areas of the two
A rectangle is three times as long as it is wide. Find the dimensions of this rectangle if its area is numerically triple its perimeter.
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid
The graph of f(x) = ax2 + bx + c is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros off. Is the discriminant for the equation ax2 + bx + c = 0
The graph of f(x) = ax2 + bx + c is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros off. Is the discriminant for the equation ax2 + bx + c = 0
A baseball is hit straight up with an initial velocity of v0 = 96 feet per second (about 65 miles per hour) and leaves the bat with an initial height of h0= 2.5 feet. (a) Write a formula s(t)
A stone is thrown downward with a velocity of 66 feet per second (45 miles per hour) from a bridge that is 120 feet above a river, as illustrated in the figure. (a) Write a formula s(t) that models
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -2 2 y = f(x)
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -3-2-1 -3 بنا 2 y
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. I =
A baseball is hit so that its height in feet after / seconds is s(t) = -16t2 + 44t + 4. (a) How high is the baseball after 1 second? (b) Find the maximum height of the baseball. Support
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -8 6 -2 2 y =
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 3x² =
Find the dimensions of a square whose area numerically equals its perimeter.
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? y=f(x) 2
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -3-2-1 2 y = f(x) 123
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. if +
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. zx + 9 = x7
A rancher plans to fence a rectangular area for cattle using the straight portion of a river as one side of the rectangle. If the farmer has P feet of fence, find the dimensions of the rectangle that
A farmer wants to fence a rectangular area by using the wall of a barn as one side of the rectangle and then enclosing the other three sides with 160 feet of fence. Find the dimensions of the
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? 2 y=f(x) 2
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 2x² +
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation.
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. x(x + 2) = -13
A large hotel is considering giving the following group discount on room rates: the regular price of $120 decreases by $2 for each room rented. For example, one room costs $118, two rooms cost $116 *
A publisher is trying to minimize its average cost per book printed (total cost divided by the number of books printed). This average cost in dollars is given by f(x) = 0.000000015x2 -0.0007x + 26,
Suppose the revenue R in thousands of dollars that a company receives from producing x thousand DVD players is given by the formula R(x) = x(40 - 2x). (a) Evaluate R(2) and interpret the
A business that produces color copies is trying to minimize its average cost per copy (total cost divided by the number of copies). This average cost in cents is given by f(x) = 0.00000093x2 -0.0145x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 16x²
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 2x² +
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. 3x² + 3 = 5x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. x² + 1 = x X
The height h in feet of a golf ball after 1 seconds is given by h(t) = 96t - 16t2. (a) Find the height of the ball after 4 seconds. Is the golf ball moving upward or downward after 4
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. zx = x+
A homeowner has 200 feet of fence to enclose an area for a pet. (a) If the area is given by 4(x) = x(100-x), what dimension maximize the area inside the fence? (b) What is the maximum
A homeowner has 80 feet of fence to enclose a rectangular garden. What dimen- sions for the garden result in the maximum area enclose by the fence?
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 6x² =
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 1- =
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 3x² =
A farmer has 1000 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 8x²=
Match the situation with the graph of the quadratic function (a-d) that models it best.The temperature after x hours in a house where the furnace quits and a repair person fixes it يا b. y d. ۲
(a) Calculate the average rates of change in I(x) = 0.6x2 + 5.2x + 29 from 2015 to 2018 and from 2018 to 2020. (b) Interpret the average rate of change from 2015 to 2018. (c) Use your
Match the situation with the graph of the quadratic function (a-d) that models it best.The cumulative number of reported AIDS cases in year x, where 1982 ≤ x ≤ 1994 يا b. y d. ۲
Match the situation with the graph of the quadratic function (a-d) that models it best.The height y of a stone thrown from ground level after x seconds يا b. y d. ۲
Match the situation with the graph of the quadratic function (a-d) that models it best.The number of people attending a popular movie x weeks after its opening يا b. y d. ۲
Global investments in $ billions in IoT can be modeled by I(x) = 0.6x2 + 5.2x + 29, where x represents years after 2015. Use I (x) to determine global investments in 2015, 2018, and 2020.
Solve for the specified variable. T²kTk² = 0 for T
Solve for the specified variable. s=-16r² + 100t for t
Find the difference quotient of f. f(x) = 1 + 2x - ²
Solve for the specified variable. S = 4m² + x² for r
Find the difference quotient of f. f(x) = 3 + 4x - x²
Find the difference quotient of f. f(x) = 5-4x²
Find the formula for a quadratic function that satisfies the given conditions.Vertex (2, 1), passing through (0, 13)
Solve for the specified variable. W = F²R for I

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