I CAN :• F IND THE VERTEX OF A PARABOL A.• F IND THE AX IS OF SYMMETRY OF A PARABOL A• F IND THE Y- INTERCEPT OF A QUADRAT IC• F IND THE DOMAIN AND RANGE OF A QUADRAT• GRAPH A QUADRAT IC US ING ITS

CHARACTER IST ICS

9-1 GRAPHING QUADRATIC FUNCTIONS

QUADRATIC FUNCTION

• A quadratic function can be written in the standard form where .• The shape of the graph of a quadratic is

called a parabola.• Parabolas are symmetric about a central

line called the axis of symmetry.• The axis of symmetry intersects a

parabola at only one point, called the vertex.

TO GRAPH A QUADRATIC:

• Step 1: Find the VERTEX•

• Step 2: Find the Axis of Symmetry

• Step 3: Find the • Plug in 0 for

• Step 4: Use symmetry to find additional points• Plug in additional around vertex

• Step 5: Connect the points with a smooth curve

EXAMPLE 1: GRAPH EACH QUADRATIC EQUATION AND STATE THE DOMAIN AND RANGE.

a.

EXAMPLE 1: GRAPH EACH QUADRATIC EQUATION AND STATE THE DOMAIN AND RANGE.

b.

EXAMPLE 1: GRAPH EACH QUADRATIC EQUATION AND STATE THE DOMAIN AND RANGE.

c.

EXAMPLE 2: IDENTIFY THE VERTEX, AXIS OF SYMMETRY, AND THE Y-INTERCEPT OF EACH GRAPH.

a. b.

MAXIMUM AND MINIMUM VALUES:

• When the graph of opens upward. • The lowest point on the graph is the minimum.

• When the graph of opens downward. • The highest point on the graph is the maximum.

EXAMPLE 3: DETERMINE WHETHER THE FUNCTION HAS A MINIMUM OR MAXIMUM VALUE AND THEN STATE THE VALUE.

a. b.

EXAMPLE 4: THE CHEERLEADERS AT LAKE HIGH SCHOOL LAUNCH T-SHIRTS INTO THE CROWD EVERY TIME THE LAKERS SCORE A TOUCHDOWN. THE HEIGHT OF THE T-SHIRT CAN BE MODELED BY THE FUNCTION , WHERE REPRESENTS THE HEIGHT IN FEET OF THE T-SHIRT AFTER SECONDS.

a. Graph the function:

b. At what height was the T-Shirt launched?

c. What is the maximum height?

d. When was the maximum height reached?

HOMEWORK

• 9.1 Pages 549-551: 5 – 12, 17 – 20, 45, 46, 63