By:Chrystal OlerichAustin PageStephanie Beeber

• Definition:o Let n be a non-negative integer and let an, an-1,...a2, a1,

a0 be real numbers with an=0.• Examples of Polynomial Functions

o f(x)=ax+b                   Linear Functiono f(x)=c                        Constant Functiono f(x)=x2                                  Squaring Function

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• Polynomial functions are classified by degree. Second-degree polynomial functions are called quadratic funtions.

• Definition:o Let a, b, and c be real numbers with a=0. o f(x)=ax2+bx+c

• Examples:o f(x)=x2+6x+2o g(x)= 2(x-1)2-3o h(x)=9+1/4x2

Don’t look confused!

• The graph of a quadratic function is called a parabola. It is a "U" shaped curve.

• All parabolas are symmetric with respect to a line called the axis of symmetry.o The point where the axis intersects the parabola is the

vertex of the parabola.

Confused?!Just ask questions!

• f(x)=ax2+bx+c opens upward.o Leading coefficient is positive.

• f(x)=-ax2+bx+c opens downward.o Leading coefficient is negative.

• Vertex: If a>0, the vertex is the point with the minimum y-

value on the graph. If a<0, the vertex is the point with the maximum y-

value of the graph.Don’t whine! If you don’t get it, just listen more!

Standard Form:         f(x)=a(x-h)2+k,    a=0 • The graph of f is a parabola whose axis is x=h and whose

vertex is the point (h,k).    No

snoozing!!

Example: Sketch the graph of f(x)=2x2+8x+7; identify the vertex and the axis of the parabola. Step 1: Write in standard form.•    f(x)=2x2+8x+7         2(x+2)2-1

o Opens upward, has a vertex at (-2,-1), is shifted downward one unit and to shifted the left two units from the graph y=2x2.  

Step 2: To find x-intercepts of the graph of f(x)=ax2+bx+c, you must solve the equation by factoring or the quadratic formula. 

        QUADRATIC FORMULA: x=-b     b2-4ac                                                  2a 

If a bear can go to the

bathroom you can remember

this!!

Graph:

x=-2

y=x2

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2

1

Here to help!!

 The vertex of the graph of f(x)=ax2+bx+c is:                            -b, f  -b             2a    2a

Example: Find the vertex of f(x)=x2+2x+4      -2,  f -b                  (-1/2)2+4(-1/2)+3=1 1/4        4      2a              

Vertex: (-1/2, 1 1/4)

Ready to put this

knowledge to use!