4A – Greatest Common Factor

4E – Vertex Form

y  ax  h   k ,

2





where a  0, and h.k  is the location of the vertex

The vertex form of a quadratic equation is useful

for both graphing quadratic functions, as well as

solving quadratic equations.

Example 1 : Sketch the graph of  3,4

y

1

x  32  4

2

1

a Down ½, over 1 in

2 each direction.

h  3

Vertex at (-3, 4)

k4

4F – Graphical Representation and

the implications of symmetry

The less well-defined form of a quadratic equation

is its factored form (assuming that it can be

factored). When in the factored form, the Zero-

Product Property has direct implications on x-

intercepts in the graphical representation.



Because of the symmetry present in a parabola,

locating the vertex of the parabola is an easy

task when the x-intercepts are known.

4F – Graphical Representation and

the implications of symmetry

In general, if a quadratic factors to the form:

f(x)=(x-a)(x-b), then the x-intercepts will be at a,

and b.

Example 1: Find the x - interceptsof

f x   x  2x  1

They are at 2, and - 1.

Example 2 : Write the equationof a quadratic

with x - interceptsof 3.5 and - 2.

 

g x   x  3.5 x   2  x  3.5x  2

4F – Graphical Representation and

the implications of symmetry

All parabolashave a line (or axis) of symmetry. When in the standardform



 f x   ax 2  bx  c , that equationof that line will always be x   2ba

Since the x - coordinateof the vertex of a parabolais on that line of symmetry,

 b  b 

the vertex will always be located at  

 2a , f    

  2a  

Example 3 : Write the equationof the axis of symmetry

for the function hx   3x 2  4 x  2

4 4 2

x    2  2 

2 3 6 3 So, the vertex is located at  ,h  

3





 3 

2

2 2 2 4 8 6

h   3   4   2  3   

3 3 3 9 3 3

4 8 6 486 2 2 2

      , 

3 3 3 3 3 3 3