Consider the following equation. y = x2 + 5x − 2 (a) State whether the axis of symmetry is a vertical or a horizontal line. horizontal linevertical line     (b) State the direction in which the parabola opens. downright     upleft

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: Match the equation with its graph. 4x2 - y2 + 4z = 0 %3D -3r 3 31 21 -3 -5 56 242 4 32

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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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: 3. Select the parabola that matches the quadratic relation y = x + 3x + 2. a. C. b. d.

A: We have to find

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 focus of the parabola y=1/2-x-1/2x^2

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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: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

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: Given an equation of a parabola (x − h)2 = 4p(y− k) or (y − k)2 = 4p(x − h), how can you determine…

A: If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is…

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Write the equation of the parabola with vertex at (-9, 0) and directrix at x = -10 a) + 9 1,2 49 b)…

A: Given

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Consider the following equation. x = 4y2 − 7y + 5 (a) State whether the axis of symmetry is a…

A: (a)

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

A: Consider the given parabola y=x2+4 and the line y=2x+2. Use online graphing calculator and sketch…

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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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: The equation of the parabola that has a vertical axis of symmetry, touches the line y= 6 and has its…

A: Your 3rd option is your correct option...detailed solution I have done step by step in…

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

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Q: For the parabola y=-4(x+1)^2 - 3, the range is...?

A: For  y=ax2+bx+c  with vertex      (x1  y1)

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

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: Graph the two parabolas y = x2 and y = −x2 + 2x − 5 in the same coordinate plane. Find equations of…

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Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

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

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Q: Find the equation for the parabola that has its vertex at the origin and has directrix at x=−1/28..

A: The standard form of equation of parabola with horizontal axis is given by the formula, y2=4px…

Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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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: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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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 x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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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: If the parabola whose equation is x = ay2 + by + c has its vertex at (3,2) and a> 0, then it has…

A: The given statement is that" if a parabola whose equation is x=ay2+by+c has its vertex at 3,2 then…

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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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: Find the equation for the parabola that has its focus at (-53/4, -7) and has directrix x = 5/4.

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

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Q: Consider the following equation. y = −x2 + 5x − 2 (a) State whether the axis of symmetry is a…

A: First of all, consider the standard form of the parabola and the given equation.Compare the form…

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.