Luttrell 2012
124
Name: ______________________
Date: _____
8k – Graphing Quadratics
Parabolas have certain defining characteristics. If we know those characteristics, then we can
use them to make graphing easier. One of the first characteristics to see is the Line of s
y
mmetr
y
.
If you ‘cut’ down that line,
y
ou would cut the parabola in halves. And each half would be a
reflection of the other. If your parabola was alread
y
graphed (see #4 from lesson 8j), then take
two ordered pairs with the same
y
-value. Find the midpoint between those ordered pairs. The
line of s
y
mmetr
y
will pass through this point so that it cuts the parabola in reflected halves. The
line of s
y
mmetr
y
will also pass through the verte
x
, which is lowest point or highest point on the
graph. If the parabola were a string necklace, the verte
x
would be where the single charm would
hang. Without the graph, some refer to the equation
y
=
ax
2
+
bx
+
c
and determine the verte
x
x
-
coordinate with the formula:
x
b
a
= −
2
. Then the
y
can evaluate for the
y
-coordinate. Another
quick calculation is done to find the
y
-intercept, where the parabola crosses the
y
-a
x
is. Evaluate
for
y
when
x
= 0.
Y
ou’ll notice that
y
-value is the same as
c
in
y
=
ax
2
+
bx
+
c
. Reflect the
y
-
intercept over the line of symmetry to get another point. With those three points,
y
ou can graph.
You can always check
y
our work by knowing the direction of the parabola. From lesson 32a,
y
ou’ll notice that when
a
is positive the parabola opens upward. When
a
is negative, it opens
downward.
Graph the following equations:
1.
y
=
x
2
+ 4
x
+ 4
2.
y
=
x
2
- 6
x
+ 8
3.
y
=
x
2
- 6
x
+ 4
direction: up
y
-intercept:
y
= 0+0+4
(0,4)
verte
x
:
x
= −
= −
4
2 1
2
( )
y
= 4 +4(-2)+4 = 0
(-2,0)
s
y
mmetr
y
point: (- 4,4)
4.
y
=
x
2
+ 8
x
+ 15
5.
y
=
-x
2
+ 3
x
- 2
6.
y
=
-x
2
+
x
+ 12
