What are the coordinates of the vertex of the parabola given the function f(x)=x^2+8x-3

Q: Find the slope of the graph of the function at the given point.

A: Given: fx=3x2-4x Given point is 1, -1

Q: For square root functions sho

A: Given,       f(x)=--(x+4)

Q: Determine the equation of the cubic function that has roots at -3, -5, and 3 and passes through the…

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Q: A farmer needs to take a rectangular plot of land and divide it into 6fields of equal area. He has…

A: First of all, construct the diagram as per the question.Let, l = length of the field. b = breadth…

Q: Find three positive numbers whose sum is 600 and whose product is a maximum. Answer (separate by…

A: Given that the sum of three numbers is 600 and their product is maximum. We need to find these three…

Q: Find two positive numbers whose product is 100 and whose sum is a minimum.

A: Suppose numbers are x and y then  xy=100    ....(1)

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Find two numbers whose sum is 40 and whose product is a maximum.

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Find two positive real numbers such that the sum of the first number squared and the second number…

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Q: Ex+ 8x3-72x?+4 三X'

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given 2300m of wire is used for fencing three sides and one side is covered by river

Q: Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: First make equation and then differentiate

Q: By cutting away identical square from each corner of a rectangular piece of cardboard and folding up…

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Q: The graph of a square root function has a domain of (0, ∞) and range of [1, 0). In two or more…

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Q: Consider a parabolic arch whose shape may be represented by the graph of y = 9 - x2, where the base…

A: Pick a point P at the considered arc,  that is                         p = x , 9-x2…

Q: Solve using optimization 2. Find a pair of non-negative number that have a product of 162 and…

A: Solved below

Q: suppose the yo-yo string is 28 inches and it completes one revolution in 3 seconds. If the closest…

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Q: Find the dimensions of the rectangle of maximum area which can be laid out within a right triangle…

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given: Length of wire for electric fencing is 2000 m, and one side of plot is bounded by a river. To…

Q: A farmer has 600m of fence to enclose a rectangular divided pasture adjacent to an existing wall. He…

A: In question given that  farmer has 600m of fence to enclose a rectangular divided pasture adjacent…

Q: Find two positive numbers whose product is 100 and whose sum is a minimum. (This is optimization…

A: Let's assume two positive numbers are a and b Now, We know that for two positive numbers a+b2≥ab…

Q: A rectangular plot of ground is 120 m long and 80 m wide.To double the area of the plot,while…

A: For Rectangular plot,  Length = 120 m Breath = 80 m

Q: Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a…

A: topic- application of derivatives

Q: Find two numbers whose sum is a if the product of the square of one by the cube of the other is to…

A: Consider the first number be 'x'. The second number be 'y'. The sum of the numbers is given by a.…

Q: A wire of length L- 100cm is divided into two parts. One forms a circle and the other forms a…

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Q: 4=-Y36x-4)'+2 (4,2). Equation #15 maximum or minimum

A: Given function is,

Q: The number 72 is to be represented as the sum of two positive parts, such that the product of one of…

A: Let the two numbers be: x and y Therefore we have to maximize:  f(x, y)=x y3 subjected to…

Q: a rectangular property has three sides fenced in against an existing river by 1,200 feet of wooden…

A: Consider the given information.

Q: Is the point (3, 12) on the graph of the function g(x) = x2 + 5x - 10?

A: Given function, g(x)=x2+5x-10

Q: A rectangle is constructed with its base on the​ x-axis and its upper two vertices on the parabola y…

A: Given informationRectangle base is on x axisTop on parabola

Q: What positive number exceeds its cube by the maximum amount?

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Q: Find the two numbers whose sum is 15 if the product of the square of one by the cube of the other is…

A: Let us consider one of the numbers to be x. So, the other number will be 15-x. Now, the function…

Q: Find two numbers whose sum is 20 and whose product is a maximum

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Q: Find an equation for the graph sketched below 구 -5 -4 -3 -2 -1 4 5 -4 -5 -- -구 f(x) =

A: Explanation of the answer is as follows

Q: A rancher with 800 ft of fencing wants to enclose a rectangular area and then divide it into three…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: A rectangle is bonded by the X axis and the Parabola f(x)=16 - 0.25x^2. What length and width should…

A: NOTE: Refresh your page if you can't see any equations. . the length of the rectangle is  and the…

Q: Find the dimensions of a rectangular lot with perimeter of 300m and whose area is maximum. Use…

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Q: Find the location of the absolute maximum and absolute minimum of the function on the interval [ -…

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Q: One of your classmates makes the claim that the solution of an optimization problem modeled by a…

A: Given: Claim: The solution of an optimization problem modeled by a quadratic function occurs at the…

Q: A rectangle with horizontal and vertical sides has one vertex at the origin, one on the positive x-…

A: consider an arbitrary point on line  2x+y=100 is   x , 100-2x which is the one of the vertex of the…

Q: Find two numbers whose sum is 11 and whose product is a maximum.

A: Let x and y be the two numbersx+y =11y =11-xProduct is maximumTherefore, xy is maximumx(11-x) is…

Q: Write the equation of the quadratic function with vertex (2,-4) passing through point (0,6).

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Q: What is the maximum product of two numbers that add to 28? What numbers yield this product?

A: Given query is to find two numbers that add to 28 and their product will be maximum

Q: Find a quadratic function that fits the set of data points. (0,- 6), (5,24), (25,44) f(x) = (Use…

A: Consider a general quadratic equation of the form y = ax2+bx+c. Put all three point in the quadratic…

Q: Find two positive numbers whose sum is 9 and the product of one number and the square of the other…

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Q: Find a function whose graph is a parabola with vertex (5, −2) and that passes through the point (4,…

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other sides by a…

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Q: Find three positive numbers whose sum is 400 and whose product is a maximum. Answer (separate by…

A: Let the three numbers be x, y, z. The sum of numbers = 400. Therefore, x+y+z= 400.…

Q: A rectangular plot of land will be fenced into three equal portions by two dividing fences parallel…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.