9.3 Graphing Quadratic Functions

Quadratic Functions

Quadratic functions are functions written in the form

Every quadratic function has a U-shaped graph called a parabola.

2y ax bx c

Axis of Symmetry

Vertex

y = ax2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point.

Positive a = smiley face

If the leading coefficient is positive, the parabola opens up, like a U.

Axis of Symmetry

Vertex

y = ax2 +bx + c When a<0, the parabola opens down. The vertex is the maximum point.

Negative a = Sad Face

If the leading coefficient is negative, the parabola opens down, like an upside-down U.

Parabolas

The lowest/highest point on a parabola is called the vertex.

The axis of symmetry is the line that runs through the vertex and divides the parabola in two symmetric parts.

The x-coordinate of the vertex, and the equation of the axis of symmetry will be the line

x = -b

2a

2y ax bx c

GRAPHING QUADRATIC EQUATIONS Make a table

 

Plot points and connect dots to make a smooth curve. 

2y ax bx c

X Y

Quadratic Functions will be in the form

y = ax2 + bx + c or f(x) = ax2 + bx + c

The graph of a Quadratic Function will be a parabola.

y = x2

Use the table with the given values for x to find f(x). Then graph the function

X Y

-2

-1

0

1

2

y = 2x2

y = -2x2

Graph each function, and compare them to the graph of y = x2

y = 5x2

y = ¼ x2

X Y

-2 20

-1 5

0 0

1 5

2 20

X Y

-8 16

-4 4

0 0

4 4

8 16

y = x2

y = 5x2

y = ¼ x2

Do you notice any patterns here?

As the coefficient (a) of x2 gets larger, the graph gets narrower;And if the coefficient is less than 1, the graph is wide.

Homework

Section 9.3Page 521, # 5-10, and # 11,12,14,15,19

Plus, Box and Whisker Question on Handout (See page 375)BONUS: Do p. 378, #8-10,#15-17