Intermediate Algebra (11th edition)

59. (a)Use the graph to estimate spending on physician and clinical services in 2005 to the
    nearest $10 billion.
    (b)Use the model to approximate spending to the nearest $10 billion. How does this
    result compare to your estimate in part (a)?
    60.Based on the model, in what year did spending on physician and clinical services first
    exceed $350 billion? (Round down for the year.) How does this result compare to the
    amount of spending shown in the graph?
    61.Based on the model, in what year did spending on physician and clinical services first
    exceed $400 billion? (Round down for the year.) How does this result compare to the
    amount of spending shown in the graph?
    62.If these data were modeled by a linearfunction defined by would the
    value of abe positive or negative? Explain.

Find each function value. See Section 3.6.

65.Graph ƒ 1 x 2 = 2 x^2 .Give the domain and range. See Section 5.3.

ƒ 1 x 2 =x^2 + 4 x-3. Find ƒ 122. ƒ 1 x 2 = 21 x- 322 +5. Find ƒ 132.

PREVIEW EXERCISES

ƒ 1 x 2 =ax+b,

SECTION 9.5 Graphs of Quadratic Functions 531

Spending on Physician and Clinical Services

Source: U.S. Centers for Medicare and Medicaid

Services.

Year

Billions of Dollars

500

400

300

200

100

0

2000 2001 2002 2003 2005 2004 20062007

OBJECTIVES

Graphs of Quadratic Functions

9.5

1 Graph a quadratic
function.

2 Graph parabolas
with horizontal and
vertical shifts.

3 Use the coefficient
of x^2 to predict the
shape and direction
in which a parabola
opens.

4 Find a quadratic
function to model
data.

OBJECTIVE 1 Graph a quadratic function. FIGURE 5gives a graph of the sim-

plest quadratic function,defined by This graph is called a parabola.(See

Section 5.3.) The point the lowest point

on the curve, is the vertexof this parabola. The

vertical line through the vertex is the axisof the

parabola, here A parabola is symmetric

about its axis— if the graph were folded along

the axis, the two portions of the curve would

coincide.

As FIGURE 5 suggests, xcan be any real

number, so the domain of the function defined

by is Since yis always non-

negative, the range is 3 0, q 2.

y= x^21 - q, q 2.

x= 0.

1 0, 0 2 ,

y= x^2.

–2^02

2

4

Vertex

Axis

x

y

y = x^2

FIGURE 5

xy

4

1

00

11

24

• 1


• 2