1. Find the coordinates of the vertex of the given function using two methods: a) Completing the square method: f(x) = 3x2 + 12x - 8 %3D

Q: find the coordinates of the vertex for the parabola defined by the given quadratic function  f(x)=…

A: At the vertex x= -b/(2a)  We compare f(x)= -x^2-4x+10 with f(x)= ax^2+bx+c  a=-1 , b=-4 and c=10

Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

A: Given:   C(x) = 32,000+60x and R(x) = 130x-0.001x^2

Q: Find the minimum point for the function f(x) = 5x – 14x2 – 11x + 1

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Q: To put the quadratic function f(x)= ax2 + bx + c instandard form, we complete the____ .

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Q: Given U = VXY; and Px=10 , Py-20, income=100; what is the value of MRSxy at the optimization point?…

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Q: Complete the following questions and submit them to the dropbox. 1. Find the minimum value of the…

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Q: Find the maximum or minimum value of the quadratic function g1x2  2x2  6x  3.

A: The given quadratic function is g(x)=2x2+6x+3

Q: 2. Find the local and the absolute maximum and the minimum values Ax) = x4 – 8x3 + 6x² + 40x + 3 %D…

A:

Q: A company estimates that its profit, P, in hundreds of dollars, is P(x) = -4x2 + 40x + 3 where x is…

A: Given:     P(x) = -4x2 + 40x + 3

Q: Consider the following quadratic function. f(x) = −4x2 + 6x − 8 Find the vertex. (x, y)=

A: To determine the vertex of the equation.

Q: Given that f is a quadratic function with minimum f(x) = f(1) = 3, find the axis, vertex, range and…

A: Given, f is a quadratic function with minimum f(x) = f(1) = 3. We have to find the axis, vertex,…

Q: Find the minimum  of the function f(x) = 2x3 + 3x2 − 12x + 17

A: We have to find the minimum of the function f(x)=2x3+3x2-12x+17.

Q: 4. a. Use the vertex formula to determine the vertex of f(x) = 2x + 12x + 19. b. Based on the…

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Q: Find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = 2x2 -…

A: Given quadratic function, fx=2x2-8x+3 let y=2x2-8x+3 We know that for any parabola in the form…

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

A: f(x) = x² + 8x - 3 Let, y = f(x)  So, y = x² + 8x - 3   Next, we will complete the square on the…

Q: The area A of a triangle with two sides of equal length a is given by A = /P(P- a)²(P – b) where b…

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Q: Given that f is a quadratic function with minimum f(x) = f(2) = 5, find the axis, vertex, range and…

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Q: The revenue from the sale of a product is given by the function R= 289x-x², (a) Use factoring to…

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Q: 1. To put the quadratic function f(x) ax? + bx + c in %3D standard form, we complete the

A: Fill the blank

Q: by graphing the standard quadratic function f(x)=x². Then use transformations of this graph to graph…

A: Please refer to the image below

Q: Consider the following quadratic function 3x2 12x + 19 f(x) Find the vertex (х, у) %3 Determine…

A: Given:

Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.

Q: Please see image attached, thank you

A: Revenue function and cost function are Profit function is

Q: - Discuss the maximum and minimum of x + y +6x+12. .2

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Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the…

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Q: What is the local maximum and minimum of the equation f(x)=x2e17x

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Q: Find the minimum and maximum of y = f(x) = x³ – x² – 3x + 2

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Q: a company that makes and sells digital cameras has found that the total weekly cost of producing…

A: We have given the cost function C(x)=0.5x^2-210x+26250

Q: Find the vertex of f(x) = x² – 6x + 3 by completing the square. Show your work.

A:

Q: The annual total revenue for a wis given by R(x)=24,000x-6x^2 dollars, where x is the number of…

A: To find maximum no of units sold. Also to find maximum possible annual revenue.

Q: Find the x coordinate of the vertex: f(x)= 3x-4x+1 %3D

A:

Q: . Suppose the revenue, in dollars, for producing x chairs is given by r(x) = 90x and the cost to…

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Q: Find the minimum Cost of C(x) = 24x^2 - 820x.

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Q: Callaway Golf Company has determined that the marginal cost C of manufacturing x Big Bertha golf…

A: The marginal cost C of manufacturing x is given by the equationC(x)=4.9x2-617.4x+19600

Q: Discuss the maximum and minimum of x2+y2+6x+12

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Q: Find a quadratic function f whose graph matches the one given.

A: Find a quadratic function f whose graph matches the one given.

Q: 13) Given f(x) = 7x² – 4x – 2, without graphing, determine whether it has a maximum value or minimum…

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Q: I want solve it in а раper 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy - 2y = 0

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =…

A:

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =…

A: Given: f(x) = -2x2 + 8x - 1

Q: 3. The cost for making x gizmos is C(x) = x2 - 8x + 30. How many gizmos should be made to minimize…

A: Given C(x)=x2-8x+30

Q: A rectangular box for a new product is designed in such a way that the Three dimensions always have…

A: Given: A rectangular box for a new product is designed in such a way that the Three dimensions…

Q: 4) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in…

A: Maximum number of mosquitoes

Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

A: Let, x denotes the half width of the rectangle.y denotes the height of the rectangle.And…

Q: Find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = 2(x -…

A: For y=a(x-h)2+k vertex (h,k)

Q: Given that f is a quadratic function with minimum f(3) = 6, find the vertex, range, and…

A: The known fact is that any quadratic function represents a parabola equation having vertex as its…

Q: (b) Show that if r (x) = 6x and c (x) = x – 6x² +15x are your revenue and cost functions, then the…

A: Answer for 2(b) b) Show that if r(x)=6x and c(x)=x3-6x2+15x are revenue and cost functions, then we…

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Q: a) Find the maximum or minimum value of the given quadratic function f(x) = x + 6x +9.

A: We can find the minimum value as below