Find the vertex and opening of the parabola 1. y = 2x^2 − 2 and y = x^2 + x

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: Find the equation of a parabola with vertex on the line y = 2X, axis parallel to the x- axis and…

A: The equation of parabola parallel to horizontal axis is  x=(y-k)2+h --------------------(1) The line…

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: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

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Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

Q: What is the equation in vertex form of a parabola with a vertex of (-3, 4) that passes through the…

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

A: We have to find the equation of the parabola with vertex (−3,1) and y-intercept (0,2).

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

A: Given: Vertex (2,4)

Q: 13. Write the equation of the parabola with x- intercepts at ( 3,0) and (9,0) that passes through…

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Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: Which point on the graph of the parabola y 4x has the minimum distance between the graph and the…

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Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: 5. The equation of a family of parabolas with axis paralel to the y-axis is

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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: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: The vertical line passing through the vertex of a parabola iscalled the_________

A: Solution:GivenThe vertical line passing through the vertex of a parabola is called the ...........

Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: Find an equation of the parabola with vertex (−4, −2) and directrix y=−7.

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Q: Sketch the parabola and line on the same graph. y = 3x2 − 4  and  y = 2x + 4

A: point out zero of function and line and draw graph using these points

Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Find the equation of a parabola that has a vertex of (-2, -1) and contains the point (0, 3).…

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Q: Find an equation for the hyperbola that satisfies the Vertices: (±1, 0), asymptotes: y = ±3x

A: Given,        Vertices: (±1, 0)    asymptotes: y=±3x

Q: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

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Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: 2. A parabola with axis parallel to the x-axis and passing through (5,4), (11, –2) and (21, –4)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: · Write an equation for the parabola with vertex at (4, –1), opening upward, and with a vertical…

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Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: The rectangle has its base on the x-axis and its other two vertices above the x-axis and lying on…

Q: Find the equation for the hyperbola that asymptottes (y - 3) = +- 1/square root of 2 * (x+3) and…

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: Find the dimension of the rectangle of maximum area that can be inscribed in the ellipse…

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Q: Determine the maximum area of a rectangle with one side on the -axis and the opposite corners…

A: The formula for the area of a rectangle is length multiplied by breadth. A=l·b, where l represents…

Q: Find the Equation of a Quadratic (Parabola) Given 3 Points y=a^2+bx+c (0,0), (-3,3), (3,3) Also,…

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Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…