2.10

Graph y = ax

2

+ c

2.10-2.11 Quiz: Friday Midterm: March 11

Vocabulary

• A

quadratic function

is a nonlinear (not a line) function that can be written in the standard form

y = ax 2 + bx + c

where a ≠ 0 • Every quadratic function has a

U-shaped

graph called a

parabola

.

Vocabulary

• The

most basic

quadratic function in the family of quadratic functions, called the

parent quadratic function

, is

y = x 2

X -2 Y = 4 -1 1 0 0 1 1 2 4

Parts of a Parabola

• The lowest or highest point on a parabola is the

vertex

. • The line that passes through the vertex and divides the parabola into two symmetric parts is called the

axis of symmetry

.

Graph y = ax

2 • The coefficient “a” can stretch or shrink the graph.

• If “a” is negative then the graph flips upside down. (Or as I like to call it…makes a SAD face)

Example 1:

• Graph y = 2x 2 . Compare the graph with the parent function, y = x 2 .

– You need to make a table of values. X Y = -2 -1 0 1 2

You Try:

• Graph y = 1/2x 2 . Compare the graph with the parent function, y = x 2 .

X -2 -1 0 1 2 Y =

Example 2:

• Graph y = -3x 2 . Compare the graph with the parent function, y = x 2 . – You need to make a table of values. X Y = -2 -1 0 1 2

Graph y = ax

2

+ c

• The constant “c” moves the graph up or down.

– If “c” is positive it moves the graph up – if “c” is negative it moves the graph down.

Example 4:

• Graph y = x 2 + 2. Compare the graph with the parent function, y = x 2 . – You need to make a table of values. X -2 -1 0 1 2 Y =

You Try:

• Graph y = x 2 – 4. Compare the graph with the parent function, y = x 2 .

Homework:

• P. 100 # 1-9all, 16, 17, 20, 21