On one set of coordinate axes, graph the family of parabolasf(x) = x2 + 2x + c for c = - 3, c = 0, and c = 1.Describe the characteristics of a member of this family.

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

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Q: What is the vertex equation of a parabola with a vertex at (-5,-8) that has been reflected about the…

A: It is given that the vertex of the parabola is -5,-8. It is given that the equation of parabola…

Q: Which point on the graph of the parabola y= 4x2 has the minimum distance between the graph and the…

A: To solve this question find a function in 'x' using the distance formula equate the derivative of…

Q: Find an equation of the parabola with vertex (-1, 3) and directrix y = -3. ローロ

A: Topic:- parabola equation

Q: Which point on the graph of the parabola y = 5x² has the minimum distance between the graph and the…

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Q: How would I find the maximum value of this parabola if the velocity is 23.4305?

A: Given equation - y = -16x20.43v2+1.15x+8Differentiating on both sides with respec to x - dydx =…

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: The equation of a family of parabolas with axis parallel to the y-axis is

A: We will find the equation of family of parabolas with axis parallel to the y-axis .Below find the…

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: Find an equation of the parabola with vertex (5,-5) and directrix y=-3   .

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Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: Determine the equation of parabola that opens upward with bertex (-12,-6) with directrix y=-17.…

A: We have to find the equation of parabola whose vertex is -12, -6 and directrix is y=-17 . Clearly,…

Q: Find the equation of the parabola with vertex at (2,-1), axis is parallel to the y-axis and passing…

A: Equation of parabola parallel to y axis is given by as: (x-h)²= 4a(y-k)

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: On one set of coordinate axes, graph the family of parabolasf(x) = x2 + bx + 1 for b = - 4, b = 0,…

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Q: On one set of coordinate axes, graph the family of parabolas f(x) = x2 + bx + 1 for b = - 4, b = 0,…

A: Consider the given general form of the equation. fx=x2+bx+1 Put b=-4 in the equation. fx=x2−4x+1 Put…

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: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

A: Vertex of the parabola is h, k=0, 5 & it passes through the point 2, -3. Now the equation of the…

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: What is the equation of the parabola that has a max of (2,3), and passes through point (, -1)?

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Q: Give 3 points that lie on the parabola y=x^2-5x-2

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Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of 231, which…

A: Given   Vertex of a parabola (x,y)=(-5,6)           Y- intercept c=231

Q: Find the equation of a parabola whose vertex is located at (2, −3) and whose focus is located at…

A: Given: vertex: 2,-3focus: 0,-3 To Find: Equation of a parabola. Concept: Horizontal…

Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

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 an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Here we find the equation of parabola.

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A parabola has its turning point at x = -4 and one of the x-intercepts is x = -3. What is the x…

A: Given Data: The x coordinates of the turning point of the parabola is: x=-4 One of the x-intercepts…

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 equation for the parabola that passes through the point (-2, -4), with vertex at (3,1) and…

A: Given

Q: Write an equation of the parabola, in vertex form, that is a) Narrower than y=3x2 and is translated…

A: Find your answer below

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: What is the equation of the parabola with vertex (1, –11) and that passes through (–4, 64)?

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Q: What is the equation of the standard parabola with its vertex at the origin that opens downward?

A: we have to find the equation of the standard parabola with its vertex at the origin that opens…

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

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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: Write the equation for a parabola with vertex: (-2, 4) and directrix: x= -3

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Q: Find an equation of the parabola that is symmetric about x-axis, has its vertex at the origin and…

A: Since we know that standard equation of the parabola that is symmetric about the x-axis and has…

Q: Determine an equation of the parabola with the vertex at (-2, 5) and passes through the point (-3,…

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Q: Determine the equation of parabola with vertex (4,-5) and goes through the point (-1,-3).

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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)…

Q: Find the equation in standard form of a parabola whose focus is at (-3,-2) and whose directrix is x:…

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Q: Give the equation of a parabola with vertex at the origin

A: Given that vertex at the origin to the parabolaTo find equation…

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.