An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y =-x+20x, where 0sxs 20 and all dimensions are expressed in feet. On the accompanying set of axes, sketch a graph of the arch and determine its maximum height, in feet.

Q: Find the intersection points of the parabola above and the line -x+y=-4.

A: Given equation of parabola and the line are as below.

Q: 9. Sketch the parabola y =-x +8x-12, show all the intercepts, the axis symmetry and the vertex

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Q: graph the parabola y=(x-5)2-2

A: Consider the given equation

Q: Graph the parabola y = -2(x - 1)2 + 4.

A: We have given equation of parabola y=-2x-12+4 y-intercept of the parabola y0=-2-12+4=2 So,…

Q: What is the y-intercept of the graph of the parabola whose equation is y = x² – 2x- 8? A (4,0) B…

A: The point where a line or curve crosses the y-axis of a graph.  In other words: find the y value…

Q: y=x2- 3x-8

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Q: Graph the parabola. Y=x2-7

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Q: Use a graphing device to graph the parabola. x - 2y2 = 0

A: We have to draw the graph of parabola: x-2y2=0 Rewriting the equation, x-2y2=0x=2y2y2=12x So we have…

Q: Find the vertex of the parabola answer must be an ordered pair F(x)=2x2-8x+3

A: We will find the vertex by comparing with standard form of quadratic parabola.

Q: Use a graphing calculator to determine the quadratic equation for each set of three points that lie…

A: Here based on the general equation of the parabola we will calculate the quadric equation of…

Q: A parabola has an equation of axis of symmetry as x = 3, and it's optimal value is (-7) if the…

A: Axis of symmetry is:  x = 3 Optimal value is:  - 7 Therefore the vertex of the parabola is:  (h, k)…

Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) =…

A: In the question it is asked to form a parabolic equation in which the graph should have maximum…

Q: A parabolic arch has an equation of 3x 2 + y – 300 = 0. a) What is the maximum height of the arch?…

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Q: 12. (-2, 13), (1,-17), (7, 31)

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Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

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Q: FinD the asymplehes of the Cerve +y) (x+24+2) = X+94-2. 2,

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Q: Given an equation of a parabola (x − h)2 = 4p(y− k) or (y − k)2 = 4p(x − h), how can you determine…

A: If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is…

Q: Use a graphing device to graph the parabola. x2 = 16y

A: Given: x2=16y

Q: Which point is the vertex of the parabola y = 6(x+3)^2 - 5?

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Q: y = 3x? + 6x – 5

A: The given parabola is: y=3x2+6x-5...(1)

Q: Find the equation y = ax2 + bx + c of the parabola that passes through the points (-2,0), (0, –14),…

A: See attached file for a step by step explanation to find the equation of parabola.

Q: Write an equation of a parabola that has a vertex (3, 8), opens downward, and is congruent in shape…

A: All the parabola having same distance between focus and directrix is called to be congruent .Suppose…

Q: Graph the quadratic (parabola). Y=-x^2+x+6

A: We have to draw the graph

Q: 2. What is the vertex of the parabola y = (x + 6) - 9?

A: the general equation of the parabola = (x-a)^2 = 4 c (y-b)  where a and b are the vertices of the…

Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 6x…

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Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: Use a graphing device to graph the parabola. y2 = -1/3x

A: Use the parametric form of parabola. The parametric form for the parabola of the form y2=-4ax is…

Q: Find the vertex of the parabola. y = x2 + 14x + 49 Please enter your answer as an ordered pair.

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Q: Determine the standard equation of parabola X²-6x+5y=-34

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Q: Find the x intercepts of the parabola y=x^2-7

A: Given: y=x2-7                                              ..1 we know that at x-axis, y coordinate…

Q: What is the vertex of the parabola y = (x – 1)2 – 3? %3D

A: In this question to find the vertex of the parabola. So here we compare the given parabola with the…

Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: Is and directrix of the parabola: (y-7)²-6(x+9)

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Q: Find the equation of the parabola having the origin as its vertex, the y axis as its axis, and…

A: The equations  of the parabola whose vertex is at the origin and its axis is about y axis are…

Q: What is the equation of the parabola with horizontal axis, vertex (-2,1), and passes through the…

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Q: write in standard(vertex) form the equation for the parabola which has the following properties:…

A: Given, Parabola equation has zeros at x=1 and x=7. Maximum value = 12 The standard form of the…

Q: Determine the direction in which the parabola opens, and the vertex. y2-10y-x+23=0

A: Add x to both sides. So, this is a parabola of the form y=ax^2+bx+c with a=1=positive number. So…

Q: Use the table to determine the vertex of the parabola. -2 12 -1 -3 -4 3. -3 1.

A: All the given points satisfy the equation of a parabola.

Q: What is the maximum value of the parabola shown? a. -3 b. (-1,7) x c. d. 1 7

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Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

Q: intercepts

A: The x-intercepts are 5 & -3, i.e. the points are P(-3,0) & Q(5,0)  So, the maximum value…

Q: The skateboarder drops into a vert ramp, following a parabolar y=x^2- 2x-3. The slope of his path…

A: The given equation of Parabola y=x2-2x-3 is an open upward parabola with (0,-3) is a y-intercept…

Q: Write an equation in vertex form of the parabola that has the same as the graph of(x) = 4x² or g(x)…

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Q: Find the x intercepts of the parabola y=3x^2+10x+8

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Q: Graph the parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept. y = x2 + 4x…

A: Solution is given below:

Q: What is the vertex of the parabola      y=(x-1)2-9?

A: Given the equation of parabola

Q: Sketch the graph of y = x 2 - 6x + 8 by plotting the roots and the minimum point.

A: For a quadratic equation of the form ax2 + bx + c = 0✦ a> 0 ⇒ parabola is concave upwards.✦ a…

Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) =…

A: The vertex form of the parabola, y=a(x-h)2+k, where (h,k) is the vertex  Here, (h,k)=(7,4) The given…

Q: Find the equation of the parabola having the origin as its vertex, the y axis as its axis, and (-10,…

A: Here it is given that vertex of the parabola is (0,0) and y-axis as its axis,

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.