Graphing Equations by Locating Points (3.5.1)

Question 1

• One way to graph a line is to pick some x-values, substitute them into the function to find the corresponding y-values, and
graph the points.

Answer 1

• One way to graph a line is to pick some x-values, substitute them into the function to find the corresponding y-values, and
graph the points.

Question 2

• Whenever you see one variable squared and the other variable not squared, expect your graph to be a parabola. If it is the
x that is squared, the parabola will open up or down. If it is the y that is squared, the parabola will open to one side.

Answer 2

• Whenever you see one variable squared and the other variable not squared, expect your graph to be a parabola. If it is the
x that is squared, the parabola will open up or down. If it is the y that is squared, the parabola will open to one side.

Question 3

• Whenever you see a variable inside an absolute value, expect a V-shaped graph

Answer 3

• Whenever you see a variable inside an absolute value, expect a V-shaped graph

Question 4

Usually, you set up an x-y chart showing the values used.
In this example, –2, –1, 0, 1, and 2 were chosen for x. When
each value was substituted into the equation, the resulting
y-values were –3, –1, 1, 3, and 5. You can see how they are
paired in the chart.
Each x-y pair is the ordered pair (x,y) for the points you graph.
So, this line will included the points (–2, –3),
(–1, –1), (0, 1), (1, 3), and (2, 5).
Plot those points. Then you can easily draw the line.
The same technique works for more than just line graphs.
This graph shows a basic parabola, y = 3x
2
.
When you have an equation where the y is squared and the x
is not, expect a parabola that opens to one side.

Answer 4

Usually, you set up an x-y chart showing the values used.
In this example, –2, –1, 0, 1, and 2 were chosen for x. When
each value was substituted into the equation, the resulting
y-values were –3, –1, 1, 3, and 5. You can see how they are
paired in the chart.
Each x-y pair is the ordered pair (x,y) for the points you graph.
So, this line will included the points (–2, –3),
(–1, –1), (0, 1), (1, 3), and (2, 5).
Plot those points. Then you can easily draw the line.
The same technique works for more than just line graphs.
This graph shows a basic parabola, y = 3x
2
.
When you have an equation where the y is squared and the x
is not, expect a parabola that opens to one side.

Question 5

Here is an example that graphs as a “V”. One example of

the effect of the absolute value is to pair both –2 and 2 for x with 2 for y.

Answer 5

Here is an example that graphs as a “V”. One example of

the effect of the absolute value is to pair both –2 and 2 for x with 2 for y.