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

Q: On one set of coordinate axes, graph the family of parabolasf(x) = x2 + 2x + c for c = - 3, c = 0,…

A: Solution:given f(x) = x2 + 2x + c for c =- 3, c = 0, and c = 1To describe the characteristics of a…

Q: A parabola has no x-intercepts, vertex (1, -4), and is congruent in shape to the graph of y= 5x.…

A: To find the equation of a parabola that has a vertex at (1, -4) and is congruent in shape to the…

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

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Q: How do you find the intersections of a parabola and root function?

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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: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

A: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

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: Without graphing, locate the vertex and axis of symmetry of the parabola defined by f(x)=-3x2+6x+1…

A: Given- fx=-3x2+6x+1 To locate- locate the vertex and axis of symmetry of the parabola defined by the…

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: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

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: 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: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

A: The given parabolic curve is, y2 = 8x    ...(1)   It is given that the rate of change of ordinate is…

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

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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: 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: 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: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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Q: Find an equation of the parabola with vertex (2, 2) and directrix x = 8. 00 0=0 X Ś ?

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Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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

A: We have Vertex=(0,0)Directrix x=-15

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: Two small arches have the shape of parabolas. The first is the graph of             f(x) = 1 - x2…

A: We will first consider first graph function f(x) = 1-x2 and         second graph function g(x) =…

Q: Find an equation of the parabola with vertex (-5,-4) and directrx y =-11,

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Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: write in standard(vertex) form the equation for the parabola which has the following properties:…

A: Given, Parabola equation has zeros at x=1 and x=7. Maximum value = 12 The standard form of the…

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

A: Given

Q: How can we Find the slope of the parabola?

A: Let the equation of a parabola be: y^2 = 4ax

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

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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: What is the families of the curve of all Parabolas with axis parallel to the x-axis

A: The equation of a parabola with vertex at (h,k) latus rectum equal to 4a and axis parallel to X axis…

Q: Find the equation of the parabola whose vertex lies at (0,-2) and directrix at x=2

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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: Give an example of a parabola that has a maximum at the point (-1, 2).

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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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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.