For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the three noncollinear points given. (0, −4), (2, −6), (−3, −31)

Q: For Exercises 51-52, find an equation of the form y = ax? + bx + c that defines the parabola through…

A: NOTE: You have posted multiple questions, we have given an answer to the first question, if there is…

Q: vertex of parabola : (-2,1)= (h,k) x=a(y-k)²+h ✓ (-1.5, -2.3) (j,4.2)

A: Given Vertex of parabola h, k=-2, 1 Equation of parabola x=ay-k2+h Points of intersection of line…

Q: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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Q: A hiker realises that the sun is going down and she forgot her headlamp. If the surface of the…

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Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

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,…

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Q: Given the general form of a parabola x2+6x-24y+4=0, what is the x coordinate the vertex? h=_____.

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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: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

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

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

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Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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

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Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

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Q: What is the axis of symmetry of the parabola y=1/4x^2−14x+28?   A. y=28 B. x=7 C. x= -14 D. x=28

A: Given y=14x2-14x+28

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

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: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

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Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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Q: Sketch the parabola g(t) = -t2 + 4t - 3.

A: Sketch the parabola g(t) = -t2 + 4t - 3.

Q: Find the point on the sphere x2+y2+z²=529 that is farthest from the point (-7,-11,-29).

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Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that: y2+z2=1, x=0

Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

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Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: What is the vertex of the parabola y = (x – 1)2 – 3? %3D

A: In this question to find the vertex of the parabola. So here we compare the given parabola with the…

Q: Is and directrix of the parabola: (y-7)²-6(x+9)

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Consider the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2…

Q: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

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: Find the point(s) of intersection of the parabolas y =x2 andy = -x2+ 8x.

A: Definition used-      Point of intersection-           For finding the point of intersection of…

Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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Q: Suppose you are climbing a hill whose shape is given by the equation below, where x, y, and z are…

A: Solve #c

Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: The directrix of the parabola x2 – 4 y = 0 is

A: According to our guidelines we are supposed to do only one question . Kindly repost the other…

Q: For the parabola -2x 16y +4y2 + 13, for what value of y does r have a minimum?

A: This question is taken from the calculus in which we have to find the value of the y which makes the…

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: For the three points ( 1,5), (2,9) and (-1, 7), find a quadratic model y = ax + bx + c through the…

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: x2+y2=4, z=0

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that, x2+z2=4y=0

Q: What is the Axis of Symmetry of the parabola represented by y = - = -x² – 3x + 7? O x = 3 O x = -3 O…

A: The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent…

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: 10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use…

A: Given query is to find the point where tangent line to the parabola is parallel to the given line.

Q: For Exercise, determine the standard form of the parabola subject to the given conditions. Vertex:…

A: To determine the standard form of the parabola.

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

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.