This document provides examples of how to write ordered pairs for different parabolic functions to graph parabolas. It gives the ordered pairs for functions like y=x^2, f(x)=x^2+1, f(x)=2(x-1)^2, and f(x)=2(x-1)^2+3. By changing the coefficients or shifting the x-values, the ordered pairs can represent different parabolas that have the same basic shape but are stretched or shifted on the x-y plane. Writing the ordered pairs makes it straightforward to graph each parabolic function.

1. Sketching Parabola
One way of graphing a parabola is by writing the ordered pairs of a parabola.
Sample # 1
Give the ordered pairs of y=x2
These are the pairs
x -3 -2 -1 0 1 2 3
F(x) 9 4 1 0 1 4 9
How about f(x)= x2
+1
X -3 -2 -1 0 1 2 3
X2
9 4 1 0 1 4 9
X2
+1 9+1=10 4+1=5 1+1=2 0+1=1 1+1=2 4+1=5 9+1=10
Therefore the ordered pairs of f(x)= x2
+1 are
x -3 -2 -1 0 1 2 3
X2
+1 10 5 2 1 2 5 10
What if we want to know the ordered pair for
F(x)=a(x-h)2
Sample for a=2
Compare to f(x)= 2x2
and these are the pairs of x and y
x -3 -2 -1 0 1 2 3
F(x) 2x9=18 2x4=8 2x1=2 0 2x1=2 2x4=8 2x9=18

2. For f(x) = 2(x-1)2
we have these
x -2 -1 0 1 2 3 4
F(x) 18 8 2 0 2 8 18
Notice that the ordered pairs of 2x2
and 2(x-1)2
have the same values when the
number above zero is changed to 1 or we add 1 to the x values and copy the F(x)
values.
x -3+1=-2 -2+1=-1 -1+1=0 0+1=1 1+1=2 2+1=3 3+1=4
F(x) 18 8 2 0 2 8 18
How about if f(x)= 2(x-1)2
+3
To do so we are only to copy the x values and add 3 to F(x)
x -2 -1 0 1 2 3 4
F(x) 18+3=21 8+3=11 2+3=5 0+3=3 2+3=5 8+3=11 18+3=21
And finally we have
x -2 -1 0 1 2 3 4
21 11 5 3 5 11 21
Given these ordered pairs it is now easy for us to graph the parabola