Lesson 11.4 b=
F’08
Objective:=
To
graph parabolas in the form
&=
nbsp; &nbs=
p; y =3D ax2 + bx + c.=
Graphing y =3D
ax2 + bx + c
|
a > 0=
|
Opens upward
|
Vertex is a minimum=
|
|
a < 0=
|
Opens downward=
|
Vertex is a maximum=
|
Let’s find the =
vertex
by putting our equation in the form:
y =3D a(x - h)2 + k=
y =3D ax2 =
+ bx + c
y =3D a(x2=
+ ![](3D"M117Lesson11.4b_files/image027.gif")
x + ____) + c - ____
![](3D"M117Lesson11.4b_files/image028.gif")
=
y =3D a(x + ![](3D"M117Lesson11.4b_files/image029.gif")
)2 + ![](3D"M117Lesson11.4b_files/image030.gif")
The x coordinate of t=
he
vertex is x =3D ![](3D"M117Lesson11.4b_files/image031.gif")
. To find t=
he y
coordinate lets substitute in for x and
solve for y. (or you could remember that the y coordinate is
![](3D"M117Lesson11.4b_files/image032.gif")
. (you do not need to remember this) Y=
ou must
remember that the x coordinate of the vertex is =
. And you m=
ust
remember that the axis of sym=
metry
is x =3D .
1.&n=
bsp;
Graph y =3D=
-x2
+ 4x – 1
a. Determine how the graph opens _____________=
b. Find the vertex&=
nbsp; &nbs=
p; _____________
c. Find the axis of symmetry. _____________
d. Find the y intercept, and the x _____________
intercepts if
appropriate
e. Find a symmetric point, make a table and graph.<=
o:p>
![3D"[image]"](3D"M117Lesson11.4b_files/image013.gif")
&=
nbsp; &nbs=
p; ![3D"[image]"](3D"M117Lesson11.4b_files/image033.jpg")
![3D"[image]"](3D"M117Lesson11.4b_files/image034.jpg")
2.&n=
bsp;
Graph y =3D=
x2
– 2x – 3 =
;
a. Determine how the graph opens _____________=
b. Find the vertex&=
nbsp; &nbs=
p; _____________
c. Find the axis of symmetry. _____________
d. Find the y intercept, and the x _____________
intercepts if
appropriate
e. Find a symmetric point, make a table and graph.<=
o:p>
![3D"[image]"](3D"M117Lesson11.4b_files/image018.gif")
=
![3D"[image]"](3D"M117Lesson11.4b_files/image035.jpg")
![3D"[image]"](3D"M117Lesson11.4b_files/image036.jpg")
3.&n=
bsp;
y =3D 2x2
– 8x + 3
a. Determine how the graph opens _____________=
b. Find the vertex&=
nbsp; &nbs=
p; _____________
c. Find the axis of symmetry. _____________
d. Find the y intercept, and the x _____________
intercepts if
appropriate
e. Find a symmetric point, make a table and graph.<=
o:p>
&=
nbsp; &nbs=
p; &=
nbsp;
![3D"[image]"](3D"M117Lesson11.4b_files/image037.jpg")
=
&nb=
sp; =
![3D"[image]"](3D"M117Lesson11.4b_files/image038.jpg")
1. The function n(t) =3D -3t2 + 42t describes the number , =
n, of
tickets sold for a play each of t days after tickets went on sale.
a. What day had the g=
reatest
number of tickets sold?
b. How many tickets s=
old on
that day?
2. The greater of two integers minus =
the
smaller gives a
result of
20. Find the two integers so =
that
their product
is
minimized. Also find their pr=
oduct
Assign WS on 11.4
Homework Math XL 11.4=
and practice final #____-____
DUE BY ______________=
_______
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