Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 10.4, Problem 7MCQ
To determine

To find: The given equation in the standard form and the vertex, axis of symmetry, and the direction of opening of the parabola.

Expert Solution & Answer
Check Mark

Answer to Problem 7MCQ

The given equation in the standard form is x=2(y+2)2−5 , the coordinate of the vertex is (−2,−5) , the axis of symmetry is y=−2 , and the direction of opening of the parabola is right.

Explanation of Solution

Given information:

The equation of the parabola is,

  x−2y2=4y+6

Concept used:

Write the standard form of the equation of the parabola,

  x=a(y−k)2+h

The direction of opening,

  right, a>0left, a<0

The coordinate of the vertex is (h,k) , the coordinate of focus is (h+14a,k) , and the length of latus rectum is |1a| .

The equation of directrix is,

  x=h−14a

The axis of symmetry is,

  y=k

Write the standard form of the equation of the parabola,

  x−2y2=4y+6x=2(y2+2y+4)−8+3x=2(y+2)2−5

The direction of opening is,

  a=2>0, right

The coordinate of the vertex is (−2,−5) .

The axis of symmetry is,

  y=ky=−2

Thus, the given equation in the standard form is x=2(y+2)2−5 , the coordinate of the vertex is (−2,−5) , the axis of symmetry is y=−2 , and the direction of opening of the parabola is right.

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Chapter 10.4, Problem 6MCQ
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Chapter 10.4, Problem 8MCQ

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
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Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=dDWjhRfBsKM;License: Standard YouTube License, CC-BY
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