find the coordinates of the vertex of the parabola y=x^2-4x+1 by using the maxima and minima since the vertex of the parabola could be the minimum or maximum point. Select the correct response

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Q: Using the side of a building as one side and fencing for the other three sides, a rectangular garden…

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Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

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Q: Which point on the graph of the parabola y= 4x2 has the minimum distance between the graph and the…

A: To solve this question find a function in 'x' using the distance formula equate the derivative of…

Q: Alpha particles are deflected along hyperbolic paths when they are directed towards the nuclei of…

A: We have to find equation of path

Q: Which point on the graph of the parabola y = 5x² has the minimum distance between the graph and the…

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Q: How would I find the maximum value of this parabola if the velocity is 23.4305?

A: Given equation - y = -16x20.43v2+1.15x+8Differentiating on both sides with respec to x - dydx =…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7−x2.…

A: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7−x2.…

Q: A farmer wishes to internal vertical (y-value) fenced dividers and one internal horizontal (x-value)…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Draw the parabola y=7-x^2.

Q: A square root function passes through the point (16,-21) and has a y-intercept of -29 and a maximum…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: We need to find length and width.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 -…

A: Given equation of the parabola is,

Q: 4) A farmer has 2000 feet of fence and wants to build a rectangular enclosure along a straight wall.…

A: Given:-rectangular fence along a straight wallthere is no fence along the walltotal length of…

Q: What is the equation of the parabola which has vertex (1,2) and y-intercept y = 1?

A: See the details solution in below

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 the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: How to write the equation of the parabola with a vertex of (0,0) and axis of symmetry the y- axis;…

A: We have to write the equation of parabola with vertex (0,0) and a point in the parabola that is…

Q: Rudgene Claire, the President of Women's Association of their barangay, proposed a project: to put…

A: Give that the perimeter of the lot is 40 meter. Let x be the length of the rectangular lot  and y be…

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

A: The given parabolic curve is, y2 = 8x    ...(1)   It is given that the rate of change of ordinate is…

Q: Which point on the graph of the parabola y 4x has the minimum distance between the graph and the…

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Q: What is the equation of the parabola that has a max of (2,3), and passes through point (, -1)?

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Q: A rectangle is inscribed with its base on the xx-axis and its upper corners on the parabola y=2−x^2.…

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Q: Find the equation of a parabola that has a vertex of (-5, 8) and contains the point (-3, 12).

A: The equation of the parabola y=a(x-h)2+kwhere (h.k) is vertex .

Q: Your new puppy needs a rectangular dog run outside . You have 50 feet of fencing and plan to use the…

A: To maximize the area , we use Lagrange multipliers.

Q: x +y + 2z=1 2x-y-z = 0 x +2y-z = 4

A: Follow the steps below.

Q: Find the equation of the quadratic function whose graph is a parabola containing the points (0,4),…

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Q: Rudgene Claire, the President of Women's Association of their barangay, proposed a project: to put…

A: Let x and y be the length and width in meters be the length and width of the rectangular garden.…

Q: Find the equation of the line normal to the parabola y = x2 - 6x + 12 perpendicular to the line that…

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Q: By using the method of least squares, find the best parabola through the points: (-1,–2), (1,0),…

A: Given data: x -1 1 2 0 y -2 0 3 0 The general equation of the parabola is y=c0+c1x+c2x2…

Q: Find the rule of the quadratic funtcion whose graph satifies the following conditions: The vertex is…

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Q: Find the best parabola ax2 + bx + c that passes through the points(with minimial square error) (0,…

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Q: A man wants to fence 3 sides of his rectangular property with 1000 ft. of barbed-wire fencing. The…

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Q: In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm…

A: (2) The table containing the x and y values is shown below. x 0 30 60 90 y 23.5 37.2 35.8 19.3…

Q: Write an equation of the parabola, in vertex form, that is a) Narrower than y=3x2 and is translated…

A: Find your answer below

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

A: Length of the rectangle is 2xand breadth is y. The expression for the area of rectangle is given by…

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

A: Application of derivative problem

Q: The minimum v value of this quadratic function is 0 v At the point ( ), the x-axis intercepts with…

A: We use the data from the graph to complete the sentences. The minimum value of this quadratic…

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: The rectangle has its base on the x-axis and its other two vertices above the x-axis and lying on…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 − x…

A: Given A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y =…

Q: a box with a a square base and open top must have a volume of 62,500cm3. Find the dimensions of the…

A: Answer is mentioned below

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: Determine the maximum area of a rectangle with one side on the -axis and the opposite corners…

A: The formula for the area of a rectangle is length multiplied by breadth. A=l·b, where l represents…

Q: Determine an equation of the parabola with the vertex at (-2, 5) and passes through the point (-3,…

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Q: Give an example of a parabola that has a maximum at the point (-1, 2).

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 –…

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Q: To prevent pests, an orchard can have no more than 9 times as many apple trees as peach trees. Also,…

A: To find the number of apple trees and number of peach trees which will maximize the revenue.

Q: A rectangle has one side on the xx-axis and two vertices on the curve y=2/(4+x^2) Find the vertices…

A: Given information:A rectangle has one side on the x-axis and two vertices on the curvey=2/(4+x^2)