Section 2.1 Quadratic Functions

Today we learned all the Quadratic Functions. We learned about the definition of a Quadratic function as well as identifying the vertex of a quadratic Function by completing the square.

Definition of a Quadratic Function:

Example:

Let a,b,and c be real numbers with a not equal to 0.
f(x)=ax^2+bx+c
This is a second degree polynomial function or a quadratic function.

Standard Form of a Quadratic Function:

f(x)=a(x-h)^2+k
This equation is written in standard form.
This form is great for sketchy what a parabola looks like because it identifies the vertex of the parabola as (h,k).

Identifying the Vertex of a Quadratic Function:

Example:
Describe the graph of 2x^2+8x+7 and identify the vertex.

Solution:
f(x)=2x^2+8x+7 Write the original function so you don't get confused
f(x)=2(x^2+4x)+ 7 Factor the 2 out of the x terms
f(x)=2(x^2+4x+4-4)+7 Now you have to use (b/2)^2. SO add and subtract 4 within the parentheses
f(x)=2(x^2+fx+4)-2(4)+7 Regroup Terms
f(x)=2(x+2)^2-1 Write the equation in standard form.

To find the x-intercepts solve the equation f(x)=ax^2+bx+c