Graphing Quadratic Functions A quadratic function is an equation of the form: y = ax 2 + bx + c

How long does a firework stay in the air?

What is the hang time of a football?

How does a satellite dish work?

The graph of a quadratic function is called a parabola. It looks like a U or an upside down U.

Gallileo was the first to show that the path of an object thrown in space is a parabola.

Graphing A Parabola xy = x 2 – 2x – 3y To graph a parabola we create a table of values and then plot the points. Lets Graph: y = x 2 – 2x – 3

y = x 2 – 2x – 3 xy

Graphing A Parabola Lets Graph: y = -x 2 + 2x + 1 xy = -x 2 + 2x + 1y

y = -x 2 + 2x +1 xy y = -x 2 + 2x + 1

Vertex (Turning Point) Quadratic Equation: y = ax 2 + bx + c  The maximum or minimum point is called the vertex or turning point of the parabola.  If a is positive the graph looks like a smile. (Minimum)  If a is negative the graph looks like a frown. (Maximum)

Axis of Symmetry  The line that divides a parabola directly in half is called its axis of symmetry.  The axis of symmetry and vertex (turning point) can be found using the equation:

Golden Gate Bridge The cables that act as suspension are parabolas.

3) y = -x 2 + 4x – 1 Vertex is at: y = -x 2 + 4x – 1 xy y = ax 2 + bx + c

y = -x 2 + 4x – 1 xy Vertex? Max or Min? Axis of Symmetry?

4) y = x 2 – 2x – 8 Vertex is at: y = x 2 – 2x – 8 xy y = ax 2 + bx + c

y = x 2 – 2x – 8 xy Vertex? Max or Min? Axis of Symmetry?

Homework Graphing Parabolas Homework #1