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Algebra I Module 8 Quadratic Tutorial 2013
供稿人: Goldade
A Quadratic function f is a function in the form:
              f(x) = ax2 + bx + c
where a,b and c are real numbers.
ex.    f(x) = 2x2 + 4x + 10
a = 2, b = 4 and c = 10
a =
a =
In the equation y = 6x2 - 3x + 8
What are the values of a, b and c?
In the equation y = 4x2 + 2x + 1What are the values of a, b and c?
b =
b =
c =
c =
Parabolas are "u" shaped graphs that open upward
or downward and are vertically symmetrical.  The
lowest or highest point of a parabola is called the
vertex.  It is the point where the curve changes
directions.
The vertex is also a point on the axis of 
symmetry.  The axis of symmetry is an imaginary
line that vertically goes through the  axis.
For this quadratic
the vertex is
(3, 4)  and the
axis of symmetry
is x = 3
Notice that the axis of symmetry is really just 
the x value.
(3, 4)
x =3
The vertex of this parabola is
(            ,               )
The axis of symmetry is
x = 
All other quadratics are derived from this.
The parent function of a quadratic is
y = x2
If the "a" term of the a quadratic, or coefficient
of the squared term, is positive, the parabola 
opens upward creating a minimum vertex.
If the "a" term of the quadratic is negative,
the parabola opens downward creating a
maximum vertex.
In the equation  y = 4x2 + x - 20, the "a" term
is positve 4.  Therefore the parabola opens
upward and has a minimum vertex.
In the equation  y = -3x2 +10x +3, the "a" term
is negative 3.  Therefore the parabola opens
downward and has a maximum vertex.
In the equation,   y = 10x2 - 3x - 4, which 
of the following are true:
 the parabola opens upward with max. vertex
 the parabola opens upward with min. vertex
 the parabola opens downward with max. vertex
 the parabola opens downward with min. vertex
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