© The Visual Classroom

Introducing Quadratic Relationsy = x2

x y

–3

–2

–1

0

1

2

3

9

4

1

01

4

9

OPENS UPWARD!!

© The Visual Classroom

y = – x2

x y

–3

–2

–1

0

1

2

3

– 9

– 4

– 1

0– 1

– 4

– 9

OPENS DOWNWARD!!

© The Visual Classroom

The shape of the curve is called a parabola.

vertex

vertex

axis of symmetry

axis of symmetry

© The Visual Classroom

The shape of the curve is called a parabola.

y value is a minimum

y value is a maximum

© The Visual Classroom

The shape of the curve is called a parabola.

x-intercepts

y-intercept

opens up

© The Visual Classroom

Parabolas Are Everywhere

The Pierre Laporte Bridge in Quebec Cityhas a center span which is in the shape of a parabola.

© The Visual Classroom

The bridge to the Island of Orléans, QC.

© The Visual Classroom

Many other types of bridges are in the shape of parabolas.

Three Rivers Bridge, QC

Rideau River, Ottawa

© The Visual Classroom

Examples of Parabolas

a bouncing ball

© The Visual Classroom

Parabolic shapes will reflect rays to one focal point.

© The Visual Classroom

Any object thrown from a high place

will fall in a parabolic curve.

© The Visual Classroom

The Flight of a Golf Ball

is a Parabolic Curve.

© The Visual Classroom

the cross sections of satellite dishes.

Parabolic curves are found on

© The Visual Classroom

Parabolic shapes will reflect

rays to one focal point.

© The Visual Classroom

Many arches are in the shape of parabolas

© The Visual Classroom

Even power lines take the shape of parabolas

© The Visual Classroom

In BusinessPrice increases can mean more revenue,

but only up to a point.

Price increase

Rev

enue