Graph Horizontal Parabolas In the following exercises, ⓐ write the equation in standard form, then ⓑ use properties of the standard form to graph the equation 279. x = −2y2 + 4y

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: 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: Convert the equation x2 - 2x - 4y + 9 = 0 to standard form by completing the square on x or y. Then…

A: Given:

Q: y=-x² - 2x-5 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A:

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: 59.) Classify the equation as a circle, parabola, ellipse, or hyperbola. 16x -9y +32x+54y-209%30…

A: We have to classify

Q: Convert the equation x2 + 6x - 4y + 1 = 0 to standard form by completing the square on x or y. Then…

A: Convert the equation x2 + 6x - 4y + 1 = 0 to standard form by completing the square on x or y. Then…

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…

A:

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: 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: Q1) Find an equation of the following parabola and sketch it where Vertex: (3,2) and Focus:(1,2)

A: Given the vertex 3,2 and the focus 1,2 of a parabola. We need to find the equation of the parabola…

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: 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: What are the coordinates of the focus of the parabola? (y-2) = -20 (x +1) -20 (x + 1) %3D Enter your…

A: Given; ( y-2)^2=-20(x+1) We have to find focus of given parabolic

Q: Determine the equation of the parabola graphed below. Enter your answer in vertex form. 4 3 1 -2 -1…

A: We can find the equation of parabola in vertex form as below

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.

A:

Q: At the memorial day fireworks celebration, a projectile is launched into the air and explodes at a…

A: Given data: The given equation of the trajectory of the parabola is y = - 4/9(x-15)^2 +100. The…

Q: A seagull sits atop a cliff and spies a fish under the water. To catch the fish, the seagull dives…

A: The given equation of path is y=2x2-28x+90.…

Q: Choose the correct.Which statement describes the equation y=-x2+6x-8?A It is a vertical parabola.B…

A:

Q: Q5:Cross section of a Nuclear cooling tower is in the shape of a hyperbola with equation…

A:

Q: (a) Find the evolute of the hyperbola x2 _y? y? =D1 a? b2

A:

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

A:

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

A:

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: From the given information it is required to calculate the equation of axis of symmetry and…

Q: A soccer ball is kicked into the air. Its height above the ground is described by the equation y = −…

A: Given y=-16x2+48x

Q: Find the equation of the parabola with the following properties. Express your answer in standard for…

A:

Q: x² - 2x +12 y +37 = 0 dentify the vertex, focus, directrix, and axis of symmetry. Hint: you will…

A: Given query is to find the vertex, focus , directrix and axis of symmetry for the parabola.

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: 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 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: Using the graph, determine the coordinates of the vertex of the parabola.

A:

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.

A:

Q: By completing the square, find the standard form of the equation of the parabola: y = x^2 + 6x + 7…

A: y=x2+6x+7 On simplification, we get y=x2+6x+9-2⇒y=x+32-2

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 36.8y = x?…

A: Equation x2=-4ay, where (a > 0) represents the equation of a parabola whose, co-ordinate of the…

Q: Determine the standard equation of parabola Show your solutions X²+2y+y-1=0

A:

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.