3. Find the coordinates of the vertex, focus, and the equation of axis of symmetry with equation y = x? + 8x + 10. Sketch the graph of parabola.

Q: find the equation of the parabola with the given properties.  Vertex (0, 0), focus (0, 2)

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Q: 21. What are the vertex, focus, and directrix of the parabola with equation y = x- 6x + 15?

A: Here we have to find the vertex, focus, and directrix of the parabola with the equation y=x2-6x+15

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: or the given equation of a parabola, determine the focus, vertex, and directrix. (x – 3)? = 32(y+ 4)…

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

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Q: Find the focus, directrix, vertex and axis of symmetry for the parabola - 12(y + 2) = (x – 2)?. -

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Q: When graphed in the xyxy-plane, what is the yy-coordinate of the vertex of the parabola with…

A: given,       the parabola with equation y=−3(x−4)(x+6)

Q: Determine: the vertex, the focus, an equation for the guideline, an equation for the axis, and the…

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Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: In a parabola, the directrix has equation x = 1 and the vertex is at (3, 1). What are the…

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Q: graph the parabola. determine the focus, vertex, and directrix  x2 = -12y  y2 = -14x  1/8 ( x -…

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Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: 2. Sketch and identify the graph of the equation a+y? - 2y-3 0 in 3D.

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Q: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the equation y =…

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Q: Vertex: (6, –8), Focus: 4

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Q: 1. Write the equation into the standard form of the equation of the parabola: y? – 2y = 8x - 1.…

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Q: What is the directrix, focus, and the vertex of the parabola if Vertex V (3, −2) and axis parallel…

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Q: Find the vertex, focus, directrix, and axis of symmetry of the parabola. (y+3)²=2(x-4)

A: Given, The parabola y+32=2x-4  We have to find vertex, focus, directrix and axis of symmetry of the…

Q: What is the equation of the parabola given:  vertex at (-5, 1) and focus at (-5, 0.5) ? Write the…

A: Given, Vertex at (-5, 1) Focus at (-5,0.5) We know that the vertex form of the parabola is,…

Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (5, 0). = x

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Q: Find the standard equation of the parabola which satisfies the given condition. Vertex (-4, 2) focus…

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Q: The __________ of a parabola is the point of intersection of the parabola and the axis of symmetry.

A: Consider the below image,

Q: If the focus of a parabola whose vertex is at the origin and which opens down is (0, -4), what is…

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Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A: Given: Corners of the reference rectangle: (8, 7), (−6, 7), (8, −3), (−6, −3); Horizontal transverse…

Q: Determine: the vertex, the focus, an equation for the guideline, an equation for the axis, and the…

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Q: Which equation represents the parabola graphed on the coordinate plane below?

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with the vertex form…

Q: Find the standard equation of the parabola which satisfies the given conditions. Vertex (−4,2),…

A: Let the vertex V (-4,2) of the given parabola is left to the focus F(-4,-1) of the parabola. The…

Q: An engineer is designing a flashlight using a parabolic reflecting mirror and a light source.  The…

A: Desining a flashlight: Position the parabola with its vertex at the origin and opening upward.…

Q: Graph the parabola y2 - 2x - 2y - 5 = 0. Give the location of the focus and the directrix.

A: We have to graph the parabola and we have to give the location of the focus and the directrix where…

Q: State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. 4x² – 3x – 8y?…

A: x2-3x-8y2-4y=14 The x2 and y2 terms have different signs and different coefficients. So, it is a…

Q: The equation of the family of parabolas with vertex and focus on the x-axis where h and k are…

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Q: Find the vertex, focus, and directrix of the following parabola. Graph the equation. (x – 2)? = 4(y…

A: Given equation of parabola, (x-2)2 = 4(y-3) Standard equation of parabola : (x-h)2 = 4p(y-k) Where,…

Q: 16. Which equation represents the given parabola?

A: We want to find the equation of given parabola.

Q: The Focus and the Directrix of the parabola (x – 8)² = 8(y – 3) are -

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Q: y = 3x² + 6x – 5

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

Q: 3) Find the vertex, focus, and directrix of the following parabola. Graph the equation. y? = 8x

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Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

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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: 2x2 + 8ху + 8у? + 12х + 24у+18 %3D 0

A: 2x2+8xy+8y2+12x+24y+18=0⇒x2+4xy+4y2+6x+12y+9=0⇒x+2y2+6(x+2y)+9=0let x+2y=tt2+6t+9=0it can rewritten…

Q: Find the vertex, focus, foci and directrix of the parabola (x-6)^2+8(y+7)=0 and sketch its graph

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

A: To determine the axis of symmetry and the vertex of the parabola.

Q: The equation of the parabola r = 4(y– 2)² is opening

A: Note: Equation of parabola Direction where it opens y=ax-h2+k and a>0 Upward y=ax-h2+k and…

Q: The focus of the parabola y? + 8x = 0 has coordinates

A: Option (4) is true

Q: What are the coordinates of the turning 3) point for the graph of the parabola whose equation is y=…

A: Turning point of parabola (vertex)

Q: Use the information provided to write the equation of the parabola. Vertex: (-5, -8) Focus: (-5, -)…

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Q: An engineer is designing a flashlight using a parabolic reflecting mirror and a light source, shown…

A: Given that, The casting has a depth of 2 inches that is y = 2 in. And the casting has a diameter of…

Q: What is the equation of the family of parabolas with vertex and focus on the y-axis? A (x- h)? = +…

A: The equation of the family of parabolas with vertex and focus on y axis

Q: d. Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (-2,…

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Q: Find the vertex, focus, and directrix of the parabola (x − 6)2 − 2( y + 7) = 0, and sketch its…

A: Given: The equation of the parabola is, x-62-2y+7=0 The above equation can be converted into vertex…

Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given: the focus of a parabola -3,5 and the directrix is y=-1 Formula: Distance between point x,y on…