Math 6A ( Periods 2 & 4)

Graphs of Equations 11-9

An equation in two variables y = x + 2      produces an infinite number of ordered pairs
If we give x the value of 1, a corresponding value of y is determined
y = (1) + 2 = 3
The ordered pair is (1, 3)

If we let x = 4
y = (4) + 2 = 6
and we get the ordered pair (4, 6)

What happens if x = 0
y = (0) + 2 = 2 ( 0, 2)
or x = -1
y = (-1) + 2 = 1 ( -1, 1)

I like to remember ordered pairs---> ( ordered, pairs)

We graphed the line on a mini graph stickie.
The line is graphed using a ruler and connecting all the points we plotted. Put arrows at each end (since a line continues with out end) and write the line's equation right above the line.


For each value of x there is EXACTLY 1 value of y.
set of ordered pairs in which no two ordered pairs have the same x is called a FUNCTION


y = x + 2
in the future you will see it written as
f(x) = x + 2
so if x = 2
f(2) = (2) + 2 = 4
if x = 5
f(5) = (5) +4 = 9



We used a three column chart to compute our ordered pairs.
Please refer to the work sheet glued into your spiral notebook for the examples we completed from the class exercises found on Page 393 -- if you were absent, please come in one morning and I will review that chart with you.


The following equations create curves that are called PARABOLAS!! Notice the difference in these equations from our previous equations
y = x² +1
when we create your three column table using integers from -2 to 2
we notice
y = (-2)² +1 = 4 + 1 = 5 ordered pair (-2, 5)
y = (-1)² +1 = 1 + 1 = 2 ordered pair (-1, 2)
y = (0)² +1 = 0 + 1 = 1 ordered pair (0, 1)
y = (1)² +1 = 1 + 1 = 2 ordered pair (1, 2)
y = (2)² +1 = 4 + 1 = 5 ordered pair (-2, 5)

When you graph this... you get a "U" shaped graph.

Remember linear equations LINEar equations are lines!
and look like y = x + 2

PARABOLAS have the form y = x² or y = -x²

Let's try
y = 2 - x²
With our 3 column table
for values of x from -2 to 2
we find
y = 2 -(-2)² = 2 -(4) = -2 and the ordered pair is (-2,-2)
y = 2 -(-1)² = 2 - (1) = 1 and the ordered pair is ( -1, 1)
y = 2 -(0)² = 2 - 0 = 2 and the ordered pair is (0, 2)
y = 2 -(1)² = 2 -1 = 1 and the ordered pair is (1, 1)
y = 2 -(2)² = 2 - (4) = -2 and the ordered pair is (2, -2)

When you graph these ordered points you find you have an upside down U
hmmm... y = -x² results in a sad face parabola
and y = x² results in a happy face parabola!!