Graph Vertical Parabolas In the following exercises, graph each equation by using its properties. 265. y = 2x2 + 10x + 7

Q: What is the length of the major axis of ellipse given by the equation X^2/81+ Y^2\144=1 ?

A: Given equation of ellipse is: x281+y2144=1

Q: In the following exercise, find the coordinates of the vertex for the parabola defined by the given…

A: Given: f(x)=3x2+18x+2

Q: What are the focus of ellipse with an equation of 4x2 + y2 = 100? a.7.90…

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Q: What are the coordinates of the focus of the parabola (y + 5) = -8(x – 4) Enter your answer by…

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Q: The Coliseum in Rome is in the shape of an ellipse whose major axis measures 620 feet and whose…

A: length of major axis 2a=620                                      a=310length of minior axis 2b =514…

Q: Graph Horizontal Parabolas In the following exercises, graph each equation by using its properties.…

A: The given equation for parabola is: x=-3y2 So, the parameters according to this parabolic equation…

Q: Graph an Ellipse with Center Not at the Origin In the following exercises, ⓐ write the equation in…

A: Consider the given equation 4x2 + 9y2 − 126x + 405 = 0 Combine like terms,…

Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: y=2x + 8x +9 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A: Equation of parabola in standard form is  y = ax²+bx+c

Q: Graph an Ellipse with Center Not at the Origin In the following exercises, ⓐ write the equation in…

A: Consider the given equation is, 25x2+4y2−150x−56y+321=0. From the equation it is very clear that, x2…

Q: y = 3x² + 6x – 5

A: The function is y=3x2+6x-5

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: The loft in Casa Batlló in Barcelona, contains a series of sixty catenary arches which closely…

A: To find width and tallness of the arch in parabolic shape

Q: Which equation represents the axis of symmetry of the graph of the parabola below?

A: In this equation x=y2 The axis of symmetry is positive x - axis as you can see the graph is in right…

Q: Find an equation of the parabola with vertex (-5, 2) and directrix y =-2. D=0 ?

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Q: Q2) Put the equation (3x2 + (y- 2)² = 3) in standard form and sketch the ellip se.

A: Given the equation of ellipse.

Q: Explain how to use y2 = 8x to find the parabola’s focus and directrix.

A: Given: y2=8x   To find: The parabola’s focus and directrix

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4. (two answers…

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where h and k are the coordinates of the…

Q: Find the equation of the evolute of the parabola y? = 12x.

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Q: What are the foci of the ellipse given by the equation x2+y2−4x+9x=23?

A: Given the equation is…

Q: What is the vertex of the parabola given by the equation (y+ 1)2 =-8x?

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Q: Find the equation of the parabola whose focus is (-2,-15/4 ) and whose directrix is y = -17/4.

A: Given focus of parabola is    -2, -154 and directrix is    y=-174

Q: (b) Find the evolute of the ellipse x2 y? =D1

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

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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: 4x' 16х — 9у* + 20

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Q: Find the equation for the parabola with vertex (-3,0) and focus (0,0).

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Q: Betty was asked to write the equation of the hyperbola with asymptotes y = +x and x-intercepts…

A: Definition used -               Equations of the asymptotes of the hyperbola are-…

Q: What is the line that cuts a parabola into two equal parts? * Your answer

A: Topic:- geography      axis of symmetry: A line that divides the parabola into two equal halves and…

Q: graph the ellipse  x2/64+y2/36=1

A: Consider the given ellipse

Q: The hyperbolic representation of a 160-meter-tall tower can be modeled by (x^2)/25 - (y^2)/225 = 1…

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Q: Find an equation of the parabola with focus (-8,5) and directnx X = 4,

A: Parabola is the locus of a point, which moves so that its distance from a point called focus and a…

Q: What is the equation of the parabola below? y (2.4) (3,1) -5

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Q: y = 3x² + 6x – 5

A: Topic - vertex form of parabola y=3(x+1)2 -8

Q: Describe how to change an equation to translate the parabola vertically

A: We can translate the parabolic equations vertically. To produce the new parabola that is similar to…

Q: Determine the equation of the parabola opens upward with vertex (-12,-6) with directrix y=-17

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Q: Q2) Put the equation (3x2 + (y – 2)2 = 3) in standard form and sketch the ellipse

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Q: Graph a Hyperbola with Center at (h, k) In the following exercises, ⓐ write the equation in…

A: Consider the function: 4x2-16y2+8x+96y-204=0  To write in the form of standard hyperbola equation,…

Q: Graph Horizontal Parabolas In the following exercises, ⓐ write the equation in standard form, then…

A: x=-2y2+4yThe given equaiton is already in standard form Lets find out the vertex of the parabola…

Q: What is the equation of the standard parabola with its vertex at the origin that opens downward?

A: we have to find the equation of the standard parabola with its vertex at the origin that opens…

Q: Graph Vertical Parabolas In the following exercises, ⓐ write the equation in standard form, then ⓑ…

A: Standard form of parabola is given by  X2=4AY (a)

Q: How is the axis of symmetry related to the vertex, focus, and directrix of a parabola?

A: See the attachment below

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

A: Given the equation of parabola

Q: I must have made an error when graphing this parabola because its axis of symmetry is the…

A: I must have made an error when graphing this parabola because its axis of symmetry is the y-axis.…

Q: Write the equation for a parabola with vertex: (-2, 4) and directrix: x= -3

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Q: Write the equation of a parabola whose directrix is y = 10.75 and has a focus at (-3, 1.25).

A: Given :focus -3, 1.25

Q: Graph the parabola, then label the vertex, axis, and intercepts. 1 Y = --x² + 2x + 4 %3|

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Q: Graph a Hyperbola with Center at (h, k) In the following exercises, ⓐ write the equation in…

A: a) We first use the completing square to write the hyperbola in the standard…

Q: Describe how the parabolas y = x2 + bx change as b changes from -oo to oo.

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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.