Luttrell 2012
123
Name: ______________________
Date: _____
8j – Graphing Quadratics
Polynomials with a general form of
y
=
ax
2
+
bx
+
c
are called quadratic equations. When a
quadratic is graphed, the shape of the curve is referred to as a parabola. One of the easiest, but
time-consuming methods of graphing a parabola is to complete a t-chart. Then plot the points.
E
x
ample: Graph
y
= 2
x
2
- 3
x
+ 1.
Start by choosing common values for x or y:
In the end it should look like:
Substitute the values you picked:
When
x
= -1, then
y
= 2 + 3 + 1 = 6.
When
x
= 0, then
y
= 0 - 0 + 1 = 1.
When
x
= 1, then
y
= 2 - 3 + 1 = 0.
When
y
= 0, then 0 = 2
x
2
- 3
x
+ 1.
Then b
y
factoring, we can solve 0 = (2
x
-1)(
x
-1) for
x
= ½ or 1.
Place the corresponding values in the t-chart. Then plot on the
axis provided. Connect the dots. The shape of the curve should
look like a
u.
Fill in the t-charts. Then graph to the right. Please label!
1.
y
=
x
2
+ 4
x
- 5
x
-5
-3
-1
0
1
3
y
2.
y
= 2
x
2
+ 3
x
- 5
x
-3
-2
-1
0
1
2
y
3.
y
=
x
2
+ 5
x
+ 6
x
- 4
-3
-2
-1
0
1
y
4.
y
=
-x
2
+ 3
x
+ 4
x
-1
0
1
2
3
4
y
x
-1
0
½
1
2
y
6
1
0
0
3
x
-1
0
1
2
y
0
