Math 41 Exam 2 Review
2.1 Quadratic Functions
You need to know the difference in the equations of linear,
quadratic, and higher degree polynomials.
The general form of a quadratic function is
2
( )
f x
ax
bx
c
=
+
+
.
The graph of a quadratic function is called a parabola.
All
parabolas have symmetry with respect to a line called the axis of symmetry.
The point at
which the axis of symmetry crosses the parabola is called the vertex.
You can think of
the vertex as being the maximum or minimum of the parabola.
Look at the parent
function chart on page 93 to review the characteristics of the graph of
2
( )
f x
ax
=
.
You
need to be able to graph a quadratic function.
The easiest way to do that is to take the
equation of the parabola from general form to standard form.
You do that by completing
the square.
To complete the square, a) group the variable terms, b) factor out the
coefficient of the x
2
term from the variable terms, c) take the coefficient of the xterm,
divide by 2 and square that.
That’s the number that you add and subtract inside the
parentheses, d) take out the subtracted term from the parentheses (making sure you
multiply it by the coefficient before the parentheses), e) compact your completed square
and combine your constants.
The standard form of the equation of a parabola is
2
( )
(
)
f x
a x
h
k
=

+
, where the coordinate of the vertex is (h,k).
You need to be able to
find the vertex and you need to be able to write the equation of a parabola given its vertex
and a point on the graph.
You need to be able to find the maximum and minimum value
of a parabola.
If a>0, the parabola has a minimum value at
2
b
a
x

=
.
If a<0, then the
parabola has a maximum value at
2
b
a
x

=
.
Understand the difference between when a
question asks you to find where the max/min value occurs (looking for x), and what the
max/min value is (looking for y!)
2.2 Polynomial Functions of Higher Degree

Remember that a polynomial function is
continuous.
That means no breaks or sharp corners in the graph.
You need to know the
Leading Coefficient Test: If
n
is even
 (If a
n
> 0, the graph rises to the left and right)(If
a
n
< 0, the graph falls to the left and right).
If
n
is even
 (If a
n
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 Fall '07
 BRUNSDEN,VICTORW
 Math, Exponential Function, Polynomials, Equations, Natural logarithm, one degree

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