Intermediate Algebra (11th edition)

NOW TRY

Completing the Square to Graph a Horizontal Parabola

Graph Give the vertex, axis, domain, and range of the relation.

Factor out. Complete the square within the parentheses. Add and subtract 1. Distributive property

Factor. Simplify.

Because of the negative coefficient in the graph opens

to the left (the negative x-direction). The graph is narrower than the graph of

because See |- 2 | 7 1. FIGURE 17.

y= x^2

- 2 x=- 21 y- 122 - 1,

x=- 21 y- 122 - 1

= - 21 y^2 - 2 y+ 12 + 1 - 221 - 12 - 3

=- 21 y^2 - 2 y+ 1 - 12 - 3

= - 21 y^2 - 2 y 2 - 3 - 2

x=- 2 y^2 + 4 y- 3

x=- 2 y^2 + 4 y-3.

1 a 12

EXAMPLE 9

SECTION 9.6 More About Parabolas and Their Applications 547

Graphing a Horizontal Parabola a 1

Graph Give the vertex, axis, domain, and range.

This graph has its vertex at since the roles of xand yare interchanged.

It opens to the right (the positive x-direction) because and has

the same shape as Plotting a few additional points gives the graph shown in

FIGURE 16.

y=x^2.

a=1 and 1 7 0,

1 - 3, 2 2 ,

x= 1 y- 222 - 3.

EXAMPLE 8 1 = 2

y y

3

2

2
1
1

2 3 1 4 0

x x

0

(1, 4)

(1, 0) x x

y y x x ((y – – 22 ))^22 – – 33

(–3, 2) y y 22 (–2, 1)

(–2, 3)

FIGURE 16

Vertex: Axis: Domain: Range: 1 - q, q 2

3 - 3, q 2

y= 2

1 - 3, 2 2

x= 1 y- 222 - 3

Be careful here.

y

3

1

2 0 1

x

0 x

y

x – 2 y^2 + 4 y – 3

(–3, 2)

(–3, 0)

(–1, 1)

FIGURE 17

Vertex: Axis: Domain: Range: 1 - q, q 2

1 - q, - 14

y= 1

1 - 1, 1 2

x=- 2 y^2 + 4 y- 3

NOW TRY

CAUTION Only quadratic equations solved for y (whose graphs are vertical

parabolas) are examples of functions.The horizontal parabolas in Examples 8 and 9

are notgraphs of functions, because they do not satisfy the conditions of the vertical

line test.

NOW TRY
EXERCISE 8
Graph.
Give the vertex, axis, domain,
and range.

x= 1 y+ 222 - 1

NOW TRY ANSWERS
8.

vertex: ; axis: ; domain: ; range:

vertex: axis: domain: range: 1 - q, - 24 ; 1 - q, q 2

1 - 2, - 12 ; y=-1;

3 - 1, q 2 1 - q, q 2

1 - 1, - 22 y=- 2

x

y

–1 0 3 –2

x = (y + 2)^2 – 1

(–1, –2)

NOW TRY
EXERCISE 9
Graph.
Give the vertex, axis, domain,
and range.

x=- 3 y^2 - 6 y- 5