Graphing quadratic functions (Section 5.1

Forms of the quadratic function Standard form

Vertex form

Intercept form

qxpxay

khxay

cbxaxy

2

2

The graph of a quadratic function is a parabola The parabola opens up if a>0 and opens

down if a<0. The parabola is wider than the shape of

the parent function if the absolute value of a is less than one, and is narrower than the graph of the parent function if the absolute value of a is greater than one.

Graphs of some quadratic functions

Using standard form of a quadratic function The x-coordinate of

the vertex is

The axis of symmetry is the vertical line

a

b

2

a

bx

2

1

122

722

x

x

xxy

Using standard form of a quadratic function(continued)

Using standard form of a quadratic function (continued)

int7,0

8,1

8

7121 2

y

vertex

y

y

Using vertex form of a quadratic function

narrowerup

vertex

xy

,

6,4

642 2

Using intercept form of a quadratic function

widerdown

x

xxy

,

int0,5,0,3

5321