Let’s Graph Parabolas
Parabola Type I 2 solutions
Y = 2x2 + 10x + 6
Step 1: Find the discriminant b2– 4AC
A= 2
(10)2 – 4(2)(6)
B = 10
100 – 48
C=6
52
Since my discriminant is positive, there are 2
solutions. The parabola will cross the x-axis twice.
Step 2: Find the solutions x=
X=
√
( )
x
–
Step 3: Plot these two points
√
Parabola Type II
1 Solution
Y = 4x2 – 12x + 9
Step 1: Find the discriminant b2– 4AC
A= 4
(–12)2 – 4(4)(9)
B = – 12
144 – 144
C=9
0
Since my discriminant is zero, there is 1 solutions.
My parabola will cross the x-axis 1 time. It will
actually sit on the x-axis
Step 2: Find the solution x=
√
√
X=
=
= 1.5
I now know the vertex…my solution has a ycoordinate of 0 and remember that the parabola
is sitting on the x-axis…so, the solution is the
vertex. (1.5, 0)
Step 3: Find two other points using symmetry
Step 4: Find the vertex x =
A) X =
B) Find Y
Y = 2(-2.5)2 +10(–2.5) + 6
Y = – 6.5
The vertex is (– 2.5, – 6.5)
X
Y
0
I choose 0 for this box
because it makes the math
easier
1.5
0
3
I choose 3 for this x-value
because it is 1.5 units away
from the line of symmetry
Now I solve for Y when X = 0 and when x = 3
Of course because of symmetry, the y when value
when X= 3 is simple.
X
0
1.5
3
Y
0
9
9
Plot the three points.
C’est fini
C’est fini
Parabola Type III
0 Solutions
Y = 6x2 – 4x + 5
Step 1: Find the discriminant b2– 4AC
A= 6
(–4)2 – 4(6)(5)
B=–4
16 – 120
C=5
– 104
Since the discriminant is a negative number, there
are no solutions. This means that the parabola will
not cross the x-axis.
Step 2: Find the vertex x =
X= =
Now go to an input/output table to find the y
coordinate of the vertex.
X
y
4
2
Y = 6(1/3) – 4(1/3) + 5
The vertex is at ( , 4 )
Step 3: Find two other points in the table, using 0 I
possible and symmetry to keep the math easier.
X
0
y
5
4
Now that I have 3 points, I am ready to graph.
5
Try these:
1) y = x2 + x + 6
5) y = – x2 – 8x – 12
3) y = x2 – 6x + 9
(– 6, 0), (–2, 0)
(– 1, 6), (0, 6)
(0, 9) , (6, 9)
2) y = x2 – x – 12
4) y = –x2 + 8x – 16
6) y = – x2 + 2x – 6
(–3, 0), (4, 0)
(0, – 16), (8, – 16)
(0, – 6), (2, – 6)