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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

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.

02

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.

03

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" $x$ $- 1$ $0$ $1$ $2$

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

04

Graph the equation.

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Most popular questions from this chapter

Solve $25 p^{2} = 49$ $25 p^{2} = 49$

Simplify each expression:

$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

In the following exercises, simplify each expression.

${(y^{4})}^{3} . {(y^{5})}^{2}$

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$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$

In the following exercises, factor completely.

$8 x^{3} - 27 y^{3}$

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