Advanced Algebra
Name __________________________________
3.1 Notes: Quadratic Functions & Models
Objective: In this lesson, you learned how to sketch and analyze graphs of functions.
Important Vocabulary
Axis of Symmetry ___________________________________________________________
Vertex _____________________________________________________________________
Definition of Polynomial Function
Let n be a nonnegative integer and let an , an1 , ..., a2 , a1 , a 0 be real numbers with an  0 . The
function given by _____________________________________________ is called a ____________
function of ____ with degree _____.
Definition of a Quadratic Function
Let a, b, and c be real numbers with a  0 . The function given by _________________________
is called the _________________ function.
A quadratic function is a polynomial function of __________ degree. The graph of a quadratic
function is a special “U”-shaped curve called a ________________.
f  x   ax 2  bx  c
f  x   ax 2  bx  c
If the leading coefficient of a quadratic function is positive, the graph of the function opens _____
and the vertex is the _______________ y-value. If the leading coefficient of a quadratic function is
negative, the graph of the function opens _____ and the vertex is the _______________ y-value.
The absolute value of the leading coefficient a determines ________________________________ .
If a is small, ____________________________________________________________________
The Standard Form of a Quadratic Function
The quadratic function given by _______________________________ is in the standard form. The
graph of f is a parabola whose axis is the vertical line _________ and whose vertex is the point
_______. If _______ , the parabola opens _____________ and if ________, the parabola opens
______________.
Remember, the x-intercepts of a quadratic function are where the graph crosses the ____________
which means that _______. So to find the x-intercepts, substitute ____ in for ____ and solve for
_____.
Example
Identify the vertex, axis of symmetry, and x-intercepts of the following equations. Sketch a graph.
f  x   2  x  3  1
2
f  x 
1
2
 x  1  2
2
For a quadratic function in the form _____________________, the x-coordinate of the vertex is __________
and the y-coordinate of the vertex is ___________.
Example
Identify the vertex, axis of symmetry, and x-intercepts of the following equations. Sketch a graph.
f  x    x 2  8 x  15
1
f  x   x 2  2 x  12
4
Example:
Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes
through the given point.
Vertex:
 3,4  Point: 1,2 
 1 3
 4 2
Vertex:   ,  Point:
 2,0