@ Solution of Quadratic Func=
tion
with Rational Roots @
A Quadratic
Function is an Algebraic equation of two variables. One variable
is a second
degree while the other is first
then usually followed by a constant.
Graph or curve (Set of Pts) of a Quadratic Function resembles a U s=
hape
curve.
One variable is calle=
d the independent va=
riable
while the other is called the
<=
span
style=3D'color:blue;mso-bidi-font-weight:bold'>dependent
variable. The independent is =
the horizontal variable while the
d=
ependent
variable is the vertical variable. Use
Gizmo to explore Quadratics!
Quadratic Functions (equations) normally appear in distinct
arrangements:
=
; Standa=
rd
Form: f(x) =3D ax2 + bx + c, A,B,C ar=
e real
numbers.
Other essential characteristics is that (a) is nonzero real number and f(x)
=3D y
=
; also, (x) is considered the Domain (H va=
lues)
while (y) the =
Range
(V values).
If
the Domain of X is real numbers then<=
/span> a Quadratic Curve will cross
the X axis twice.<=
/p>
Locate: =
Intercepts, Axis of
Symmetry, Vertex, Symmetry Point to sketch solution!
Given: y=3D =
–x2
+x –6
Determine Infinite Solution Set which is a U shaped curve!
What do
your suspect the Infinite Solution Set will look like?
Try to factor the Quadratic first to determine if it has Rational Roots or X intercepts!
Given: y =3D=
–x2
–x + 6 =3D =
(–x
+ 2) (x + 3) are factors thus x =3D –3 & x =3D +2 Rational Roots!<=
/b>
The
(X) Intercepts are – 3 and +2 while =
(Y)
Intercept is y =3D (0)2 –(0) +6 =3D +6 (0,6)=
Using
the Midpoint Formula: ( X1 + X2) / 2 =
=3D
+ 2 + – 3 =3D – 1/2 Axis of Symmetry!=
Substitute
Midpoint to locate Vertex: y =3D
(–1/2)2 – (– 1/2) – 6 =3D +1/4 + 1/2 + 6 =3D + 6 3/4<=
/p>
=
Thus: Vertex =3D (̵=
1; 1/2 ,
+ 6 1/4 ) Lo=
cate Symmetry Point by u=
sing
Axis of Symmetry!
Using
Property of Symmetry and (Y) Intercept locate the Symmetry Point! Why?
Symmetry
Point: y =3D x2
–x +6 =3D
(– 1)2 – (+ 1)
+ 6 =3D + (1) – =
(1) +
6 =3D + 6 ((0, + 6)!
=
Infinite
Solution Set of y =3D –x2 &=
#8211;x
+ 6 equals Graph
of y =3D –x=
2
–x + 6
shown below!
|
X
|
-3
|
+2
|
0
|
–1
|
–
1/2
|
|
Y
|
0
|
0
|
+ 6
|
+ 6
|
+ 6 1 =
/4
|
&nb=
sp;
=
![](3D"SolutionsQuadraticFunction2RR_files/image001.gif")
![](3D"SolutionsQuadraticFunction2RR_files/image002.jpg")
=
Tom Love =
&nb=
sp;
Malone College =
Fall 2007
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