A quadratic curve y= ax² +bx+c passes through the points (–1,4),(1,–5) and (3,5). Find the equation of the parabola.

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

A:

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

A:

Q: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

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: 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: Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes,…

A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

A:

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

A:

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

A:

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

A:

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 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: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

Q: Find the equation y=ax2+bx+c of the parabola that passes through the points (-2,0), (0,-14), (7,0)

A: The equation is:-

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 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 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…

A:

Q: Find the points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: Find the best parabola to fit the data points: (-1,1), (1, –1), (2,0), (3,0).

A: The given points are (-1,1),(1,-1),(2,0),(3,0).

Q: 5. Find the equation of the parabola that has a horizontal axis of symmetry, passing through the…

A: the general equation of a parabola is x=ay2+by+c                            (1) horizontal axis…

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

A:

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Find the best parabola ax2 + bx + c that passes through the points(with minimial square error) (0,…

A:

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

A: V-2,0

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

A:

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Find an equation of the parabola that has a vertex at (–2,3) and whose graph passes through the…

A: Equation of parabola:y=ax-h2+kWhere h,k are the coordinates of the vertexh,k=-2,3point x,y=2,19

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: 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: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product 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: Find an equation of the parabola with vertex (5, – 1) and directrix y = -4.

A:

Q: 3. Identify the vertex of the parabola y x2 + 4x + 3.

A: Here the parabola given is- y=x2+4x+3 comparing this with standard equation of parabola y=ax2+bx+cwe…

Q: Find the point on the parabola y=x2 closest to (6,3

A:

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

A:

Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

A:

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

A:

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: 6. Find the parabola y = ax² + bx +c passing through the points (–2, –6), (1, 6), and (3, 4).

A: Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points xn…

Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

A: