Quadratic Functions Polynomial Form

y-intercept x-intercept(s) Given Find Concavity Shape Vertex Axis of symmetry y-intercept x-intercept(s)

Concavity

a is positive Concavity Concave Up

a is negative Concavity Concave Down

a is positive Concavity Concave Up

a is negative Concavity Concave Down

Summary GIVEN Concave Up Concave Down

Shape

Regular

Skinny

FAT

A B Regular Regular C D Skinny FAT

A B Regular Regular C D Skinny FAT

Summary GIVEN Regular Skinny FAT

y-intercept

y-intercept When x Equals Zero ?

y-intercept When x Equals Zero

y-intercept y-intercept

Summary GIVEN y-intercept

x-intercept(s)

x-intercept(s) When y Equals Zero ?

x-intercept(s) When y Equals Zero

x-intercept(s) Graph Solutions and

Summary GIVEN x-intercept(s) Solutions to: and

ZEROS GIVEN x-intercept(s) Solutions to: and

ZEROS Same? x-intercept(s) Solutions to: and

Example Solutions to: and

Example Solutions to: and

NEVER TOUCHES THE X-AXIS NO X-INTERCEPTS

yes ZEROS x-intercept(s) NO

ZEROS x-intercept(s)

Vertex

abscissa Vertex

abscissa Vertex

abscissa ordinate Vertex

abscissa ordinate Vertex

How Do You Find Vertex

Vertex

Vertex

Vertex

Vertex

Summary GIVEN Vertex

Axis of Symmetry

Equation?

Equation?

Equation?

? Axis of Symmetry Passes Thru The Vertex

Axis of Symmetry Passes Thru The Vertex Vertex Therefore Axis of Symmetry

Summary GIVEN Axis of Symmetry

Maximum or Minimum

Concave UP RANGE Vertex

Maximum? NO Vertex

Minimum? YES Vertex

RANGE Vertex Concave Down

Minimum? NO Vertex

Maximum? YES Vertex

Summary GIVEN Maximum or = Minimum