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 3F(x) 9 4 1 0 1 4 9

How about f(x)= x2+1

X -3 -2 -1 0 1 2 3X2 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=10Therefore the ordered pairs of f(x)= x2+1 are

x -3 -2 -1 0 1 2 3X2+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 3F(x) 2x9=18 2x4=8 2x1=2 0 2x1=2 2x4=8 2x9=18

For f(x) = 2(x-1)2 we have these

x -2 -1 0 1 2 3 4F(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=4F(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 4F(x) 18+3=2

18+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 3 421 11 5 3 5 11 21

Given these ordered pairs it is now easy for us to graph the parabola