quadratics parabola (u-shaped graph)

y = ax2 y = -ax2

Sketching Quadratic Functions

A.) Opens up or down:1.) When "a" is positive, the graph curves upwards

2.) When "a" is negative the graph curves downward

3.) As "a" gets bigger the parabola gets thinner

B.)Vertex:1.) The miximum or minimum point of the parabola

2.) The x- coordinate of the vertex is

Max

Min

3.) Find the y-coordinate by plugging in the x-value into the equation

4.) Equations in the form y = ax2 (No b or c) will always have the vertex at the origin (0,0).

5.) You must label the vertex on your graph

x =

C.) Line of Symmetry

 1.) Every parabola is symmetrical

 2.) line of symmetry is a vertical line that  cuts through the vertex and divides the  curve into two symmetrical parts

 3.)

Points 2 and 3 will have the same y-coordinate

Point 4 and 5 will have the same y-coordinate1

2 3

45

Line of symmetry

4.) Formula for finding the line of symmetry;

5.) You must draw in a dotted line for the line of symmetry

x =

Answer the following questions about each quadratic equation.

ex 1: y = 4x2

opens: up or down

vertex:

Axis of symmetry:

ex 2: y = 2x2 - 10x

opens: up or down

vertex:

Axis of symmetry:

ex 3: y = -x2 - 8x + 32

opens: up or down

vertex:

Axis of symmetry:

Sketching Quadratic Functions

To sketch the graph1.) Find the vertex  (the point it changes direction)2.) Find the line of symmetry3.) Graph a.) plot the vertex b.) Set up a table of values with two points  on each side of vertex- plot the points c.) sketch the parabola

y = x2

y = -x2

y = 2x2- 4x

ex 1: y = x2 + 2x - 4