There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The parabola also passes through the x-intercept of 3x+6y-1= 0. Determine the equation of this parabola.

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 parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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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: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: Find the intersection points of the parabola above and the line -x+y=-4.

A: Given equation of parabola and the line are as below.

Q: A parabola has vertex (2,4.8) and one x-intercept is (3,0). The other x-intercept is (?,0)

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Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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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: Find the standard equation of the parabola which satisfies the given condition. Vertex (-8, 3),…

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Q: Sketch the graph of quadratic surfaces. Y=(x^2+3z^2)^(1/2)

A: We need to plot the surface: y=x2+3z2.

Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

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: 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: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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Q: What is the equation of the parabola which has vertex (1,2) and y-intercept y = 1?

A: See the details solution in below

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

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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 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: 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: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

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: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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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: Consider the equation of parabola y = 5x - 30x + 45. %3D Its vertex is located at (

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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 coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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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: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

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

A: Given, y=x2+4   y=2x+2  The graph of given functions can be plotted as shown in the figure below.

Q: Find the minimum distance from the point (4, 2) to the parabola y² = 8x. A 4/3 (B 2/2 /3 D 2/3

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

A: Given :-  Vertex (4, -7) and  x - intercept is -4 . To Find the standard equation of a parabola :-…

Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

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: Obtain the X-value of vertex for the parabola defined by y = x2 +8x - 5

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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: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

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

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

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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.