Beginning Algebra, 11th Edition

NOW TRY EXERCISE 10

Graph y=-x^2 - 1.

5.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials

The graph of is the graph of a function, since each input xis related to just

one output y. The curve in FIGURE 3is called a parabola.The point the lowest

point on this graph, is called the vertexof the parabola. The vertical line through the

vertex (the y-axis here) is called the axisof the parabola. The axis of a parabola is a

line of symmetryfor the graph. If the graph is folded on this line, the two halves will

match.

(b)

Once again, plot points to obtain the graph. For example, if then

The point and several others are shown in the table that accompanies the

graph in FIGURE 4.The vertex of this parabola is Now the vertex is the highest

point on the graph. The graph opens downward because has a negative coefficient.

NOW TRY

NOTE All polynomials of degree 2 have parabolas as their graphs.When graphing,

find points until the vertex and points on either side of it are located. (In this section,

all parabolas have their vertices on the x-axis or the y-axis.)

x^2

1 0, 3 2.

1 - 2, - 12

y=- 1 - 222 + 3 =- 4 + 3 = - 1.

x=-2,

y=-x^2 + 3

1 0, 0 2 ,

y=x^2

y

Axis

Vertex

x^2

y 3 2 1 0

1

2

3

9 4 1 0 1 4 9

x

22

4

9

0 x

y

y -x^2 3

y

2

1
0
1
2

1
2
3
2

1

x

220

(0, 3)

x

y

FIGURE 3 FIGURE 4

Complete solution available
on the Video Resources on DVD

5.4 EXERCISES

Concept Check Fill in each blank with the correct response. 1.In the term , the coefficient is and the exponent is. 2.The expression has term(s). (how many?) 3.The degree of the term is. 4.The polynomial an example of a trinomial. (is/is not) 5.When is evaluated for , the result is.

is a trinomial of degree 6.

is an example of a monomial with coefficient 8, in the variable x, having degree 5.

3 xy- 2 xy+ 5 xy=

5 x + 3 x^3 - 7 x

x^2 + 10 x= 3

4 x^2 +y^2

3 x^9

4 x^3 - 5 x^2

4 x^6

NOW TRY ANSWER
10.
x

y –1 –5

2

y = –x^2 – 1