Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and (3, 9/2).

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

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Q: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find the equation of a parabola that has a vertex of (-5, -3) and contains the point (-4, -5).…

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

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Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Write the equation of the hyperbola 9x² - 36y2 - 18x144y - 459 = 0 in standard form (x - h)² (y -…

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Q: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points…

A: We will find out the required value.

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: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

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Q: Find the standard equation of any parabola that has vertex V.

A: The equation is a statement that consists of equal symbol between two algebraic expressions. The…

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Find the equation of the parabola with vertex (2, 4) and directrix x = –3

A: Given: Vertex (2,4)

Q: Find the equation y=ax^2+bx+c of the parabola that passes through the points (-2, 0), (0, -14), (7,…

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Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

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Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: Ay 3-

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Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

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Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

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: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: Find the equation of the parabola if vertex at (1,-1) the axis of symmetry is parallel to y-axis and…

A: Equation of parabola that have an axis of symmetry parallel to y-axis and the vertex at h,k is…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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Q: Find the equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: Find the length of the hyperbola. (y-2)2/ 9 - (x+1)2/4 =1

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Q: 30. Find the vertex of the parabola y = 4x² – 4x + 3 a. 0.5,2 b. 0.5,-2 C. -0.5, 2 d. -0.5, -2

A: I have draw the graph of parabola and find that Vertex=(0.5, 2)  Hence option (a) is correct

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

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Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: ind the equation y=ax^2+bx+c of the parabola that passes through (-2,0),(0,14),(7,0

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Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

Q: What is the equation of the given parabola? y 4 -5-4-3-2 1 2 3 4 5 A y= 3x² 6x +3 I23 45

A: Here zeros form equation y=a(x-p)(x-q) p,q are zeros of equation

Q: Find the point(s) of intersection of the parabolas y =x2 andy = -x2+ 8x.

A: Definition used-      Point of intersection-           For finding the point of intersection of…

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

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Q: Write the equation of the hyperbola 9x² – 4y? – 54x + 32y – 19 = 0 in standard form (x – h)? (y –…

A: Write the equation of the hyperbola  9x2 - 4y2 -54x +32 y  -19 =0 In the standard form  (x-h)2 /a2 -…

Q: The directrix of the parabola x2 – 4 y = 0 is

A: According to our guidelines we are supposed to do only one question . Kindly repost the other…

Q: b. Find another equation of the parabola with vertex of coordinates 131 and containing the point of…

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Q: Find an equation of the parabola with vertex (4,2) and directrix x=-1

A: Find the equation of parabola:

Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…