Graph Vertical Parabolas In the following exercises, ⓐ write the equation in standard form, then ⓑ use properties of the standard form to graph the equation. 269. y = 2x2 − 4x − 2

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: Find the equation of the axis of symmetry of the following parabola using graphing technology. y =…

A: y=-3x2-18x-39 The graph is,

Q: Write the equation of the parabola with Vertex (5,1) and Directrix xr 3.

A:

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: 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: 297. 5

A: Given that, the hyperbola is x225-y29=1. Compare the equation x225-y29=1 in to standard form of the…

Q: Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse…

A:

Q: Write the equation of a hyperbola with center at the origin, passing though (±4,0) with no…

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Q: 8 -7 -6 -4 -3 to it

A:

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: Convert the equation y2 - 2y + 12x - 35 = 0 to standard form by completing the square on x or y.…

A: Consider the provided parabola equation, y2-2y+12x-35=0 Find the vertex, focus, and directrix of the…

Q: Katalin rides her bike through a tunnel shaped like the top half of an ellipse. The tunnel is 11…

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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: E. Explain what a second-degree equation in tow variables, x and y, is, and how you can ell whether…

A: Please look into the next step for details

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 ?

A:

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

A: Consider the equation is, y=2x2+10x+7 The axis of symmetry is, x=-b2a Then, x=-1022=-52

Q: ises 17–30, find the equations of the parabola

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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: Using the graph,determine the coordinates of the y-intercept of parabola

A: Introduction: A parabola is a conic section whose eccentricity is less than 1. A parabola is either…

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

A:

Q: Is it possible for two different parabolas to have the same focus and vertex? Explain with proof.

A: Actually, there cannot be two different parabolas with same focus and vertex..

Q: (b) Find the evolute of the parabola y? = 4ax.

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

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Q: Divide both sides of 4x² – 9y? = 36 by 36 and simplify. How does the simplified equation differ from…

A: Given- 4x2-9y2=36 To simplify- The above expression by dividing 36 in both sides and then state how…

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 equation of the parabola below? y (2.4) (3,1) -5

A:

Q: y = 3x² + 6x – 5

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

Q: I graphed an ellipse with a horizontal major axis and foci on the y-axis.Determine whether the…

A: Given: I graphed an ellipse with a horizontal major axis and foci on the y-axis. Determine whether…

Q: Which is the equation of the parabola with focus (0, 8) and directrix y = – 8?

A: We will use the fundamental property of parabola.

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: Write an equation of the parabola in standard form when focus is (9,0) and directrix is x=-9

A: The equation of parabola having directrix x=aand focus (a,0) is given by=y2=4ax

Q: A- Sketch the graph of ellipse: - (x-1)2 + y? = 0. 4

A: A) we use the standard forms (x-h)2a2+(y-k)2b2=1 The center of the ellipse is (h,k). Now, to compare…

Q: Write the standard form of an equation of a parabola with vertex (h, k) and horizontal axis of…

A: The standard form of the parabola, if the parabola is vertical:

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

A:

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 are the vertex and the axis of symmetry of the parabola shown in the diagram below? y

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Q: Write the equation for a parabola with a Focus (4,1) and Directrix y=8 ?

A: we know that the distance between any point on parabola and the focus is same as the distance…

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: 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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Q: y=(x-3)^2-1 how to find vertex and plot five point two on the left and two on the right for this…

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Q: (x – 4) = –12 (y + 3) - Find the vertex, focus, and directrix of the parabola.

A: The given equation is: x-42=-12y+3                                     (1)

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.