Section 2.1- Quadratic FUNctions

Polynomial functions

• Let n be a non negative integer and let   be real numbers with.

• The function is called a polynomial function of x with degree n.

• Polynomial functions are classified by degree.

• Constant function:

• It has a degree of 0.

• Linear function:

• It has a degree of 1.

• The type of polynomial function discussed in this section is the quadratic function.

Quadratic Functions

• Let a, b, and c be real numbers with
• The graph of a quadratic function is a special type of U shaped curve called a parabola.All parabolas are symmetric with respect to a line called the axis of symmetry.
• The point where the axis intersects the parabola is the vertex of the parabola.
• If the leading coefficient a is positive, the graph is a parabola that opens upward. If the leading coefficient a is negative, the graph is a parabola that opens downward.

• The simplest type of quadratic is
• In the graph a > 0, the vertex is the minnimum point on the graph; and if a < 0, the vertex is the maximum point on the graph.

• The Standard form
• , 
• It identifies the vertex of the parabola as (h,k)
• Ex: 

 (step 1)

 (step 2)

 (step 3)

Vertex = (-2, -9)

• How to complete the square
• Step 1: factor out any coefficient of that is different from 1.
• Step 2: addinside the parentheses and subtract multiplied by the coefficient of outside the parentheses.
• Step 3: simplify into standard form.