Chapter 11: Q.182E (page 1135)

In the following exercises, graph each equation.
$x = - y^{2} - 2 y + 3$

Short Answer

Expert verified

Given equation for the conic will be a parabola.

Step by step solution

Step 1. Identify the conic

Since, only one variable $y$ is squared, conic will be a parabola.

Step 2. Covert the equation into vertex form

$x = - y^{2} - 2 y + 3$

$x = - (y^{2} + 2 y + 1) + 1 + 3$

$x = - {(y + 1)}^{2} + 4$

Step 3. Find the vertex, line of symmetry, x and y intercepts of the parabola

Vertex form of the parabola is given by,

$x = a {(y - k)}^{2} + h$

Here, vertex of the parabola $\to (h, k)$

Line of symmetryrole="math" localid="1645558321060" $\to y = k$

Compare the vertex form of the parabola with the given equation,

$x = - {(y + 1)}^{2} + 4$

Since, $a$ is negative, parabola will open to the left.

Vertex role="math" localid="1645558244069" $\to (4, - 1)$

Line of symmetry $\to y = - 1$

For x-intercepts,

Put $y = 0$

role="math" localid="1645558449400" $x = - {(0 + 1)}^{2} + 4$

$x = 3$

For y-intercepts,

Put $x = 0$

$0 = - {(y + 1)}^{2} + 4$

${(y + 1)}^{2} = 4$

role="math" localid="1645558770453" $y + 1 = \pm 2 y = - 3, 1$

Step 4. Graph the equation

Graph of the equation will be,

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In the following exercises, graph each equation.
$x = - y^{2} - 2 y + 3$

Short Answer

Step by step solution

Step 1. Identify the conic

Step 2. Covert the equation into vertex form

Step 3. Find the vertex, line of symmetry, x and y intercepts of the parabola

Step 4. Graph the equation

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In the following exercises, graph each equation.x=-y2-2y+3

Short Answer

Step by step solution

Step 1. Identify the conic

Step 2. Covert the equation into vertex form

Step 3. Find the vertex, line of symmetry, x and y intercepts of the parabola

Step 4. Graph the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Statistics

Pure Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.
$x = - y^{2} - 2 y + 3$