Chapter 11: Q. 178E (page 1135)

In the following exercises, graph each equation.
$y = {(x - 1)}^{2} + 2$

Short Answer

Expert verified

Graph for the equation given will be a parabola.

Step by step solution

Identify the conic from the equation,

Equation given in the question,

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

Since, variable $x$ is squared only,

Equation will represent a parabola.

Find x, y intercepts of the graph.

For $x -$ intercept,

Put $y = 0$ in the equation.

role="math" localid="1645382935400" $0 = {(x - 1)}^{2} + 2 {(x - 1)}^{2} = - 2 (x - 1) = \sqrt{- 2}$

Since, $\sqrt{- 2}$ is not defined, $x -$ intercepts will be undefined.

Hence, there will be no $x -$ intercept.

For $y -$ intercepts,

Put $x = 0$ in the equation.

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

$y = 3$

There will be one $y -$ intercept only.

Find vertex and other points on the parabola.

Compare the given equation with the vertex form of the equation of a parabola.

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

Where, $(h, k)$ is the vertex.

Therefore, vertex of the given equation will be $(1, 2)$ .

Table for other points,

role="math" localid="1645383724764" $x$ $- 1$ $0$ $1$ $2$

$y$ $6$ $3$ $2$ $3$

Graph the equation.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, graph each equation.
$y = {(x - 1)}^{2} + 2$

Short Answer

Step by step solution

Identify the conic from the equation,

Find x, y intercepts of the graph.

Find vertex and other points on the parabola.

Graph the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.y=(x-1)2+2

Short Answer

Step by step solution

Identify the conic from the equation,

Find x, y intercepts of the graph.

Find vertex and other points on the parabola.

Graph the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.
$y = {(x - 1)}^{2} + 2$