Cambridge International Mathematics

5 Find the value(s) ofxfor which:

a f(x)=3x^2 ¡ 3 x+6takes the value 6

b f(x)=x^2 ¡ 2 x¡ 7 takes the value ¡ 4

c f(x)=¡ 2 x^2 ¡ 13 x+3takes the value ¡ 4

d f(x)=2x^2 ¡ 10 x+1takes the value ¡ 11 :

The graphs of all quadratic functions areparabolas. The parabola is one of theconic sections.

Conic sectionsare curves which can be obtained by cutting a cone with a plane. The Ancient Greek

mathematicians were fascinated by conic sections.

The name parabola comes from the Greek word forthrownbecause

when an object is thrown, its path makes a parabolic arc.

There are many other examples of parabolas in every day life.

For example, parabolic mirrors are used in car headlights, heaters,

radar discs, and radio telescopes because of their special geometric

properties.

Alongside is a single span parabolic bridge. Other

suspension bridges, such as the Golden Gate bridge

in San Francisco, also form parabolic curves.

THE SIMPLEST QUADRATIC FUNCTION

The simplest quadratic function is y=x^2 : Its graph

can be drawn from a table of values.

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y 9 4 1 0 1 4 9

Thevertexis the

point where the

graph is at its

maximum or

minimum.

Notice that:

² The curve is aparabolaand it opens upwards.

² There are no negativeyvalues, i.e., the curve does

not go below thex-axis.

² The curve issymmetricalabout they-axis because,

for example, when x=¡ 3 , y=(¡3)^2 =9and

whenx=3,y=3^2 =9.

² The curve has aturning pointorvertexat ( 0 , 0 ).

E GRAPHS OF QUADRATIC FUNCTIONS [3.2]

-2 2

4

8

x

y

@\=\!X

vertex

O

Quadratic equations and functions (Chapter 21) 431

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