Graph the following points on a Cartesian
plane. Label the 𝑥 and 𝑦 axes. Label each
point.
A. (2, 4)
B. (-3, 1)
C. (-1, -4)
D. (1, -3)
E. (0, 0)
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Section 1.1
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How can we graph functions?
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Named after French mathematician René
Descarte.
Also called Cartesian Coordinate System
Also called Rectangular Coordinate System
Has an x-axis and y-axis
The origin is the intersection of the axes
The axes divide the plane into four quadrants
Each point corresponds to an ordered pair of
two real numbers (x, y)
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For a given equation, the graph is the set of
all points whose coordinates satisfy the
equation.
One method for graphing is the pointplotting method
◦ Identify the basic shape of the graph, based on the
equation
◦ Pick an 𝑥 value
◦ Substitute it into the equation
◦ Simplify to get the 𝑦 value
◦ Plot the 𝑥, 𝑦 on a Cartesian plane
◦ Continue plotting points until you have enough to
see what the graph looks like
◦ Connect the dots
◦ Draw arrows if the graph continues
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Graph 𝑦 = 𝑥 2 + 2𝑥 − 3
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Graph 𝑦 = 𝑥 2 − 4𝑥 − 5
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The 𝒙-intercept is where the graph crosses
the 𝑥-axis. The point is (𝑥-intercept, 0)
The 𝒚-intercept is where the graph crosses
the 𝑦-axis. The point is (0, 𝑦-intercept)
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Page 121 #1-45 Every Other Odd
You MUST use graph paper.
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In Exercises 1-12, plot the given point in a
rectangular coordinate system.
1) 1,4 5)  3,5 9)  4,0
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Graph each equation in Exercises 13-28. Let
x={-3, -2, -1, 0, 1, 2, 3}.
2
13)
y  x 2
17)
y  2x 1
21)
y x
25)
y  4 x
2