You can use a graphing calculator to graph relations; however you must do some
algebra before you graph. A graphing calculator will only graph functions, so
quadratic relations that are not functions must first be written as a combination of
functions. For example, the equation of the parabola x y
2
cannot be entered
directly into the graphing calculator. We must solve the equation for y. In this
case, you obtain y
x
. To graph, you must enter the two functions y
x
and y
x
.
1 Graph the parabola whose equation is x y
2
5y 22 in the viewing
window [0, 30] by [10, 10] with scale factors of 1 on both axes.
First, solve the equation for y.
x y
2
5y 22
x 6.25 (y
2
5y 6.25) 22 Complete the square.
x 6.25 (y 2.5)
2
22 Simplify.
x 15.75 (y 2.5)
2
Subtract 22 from each side.
x
1
5
.7
5
y 2.5 Take the square root of each side.
x
1
5
.7
5
2.5 y Subtract 2.5 from each side.
Now enter the two equations y
x
1
5
.7
5
2.5 and
y –
x
1
5
.7
5
2.5 into the graphing calculator. Since both of
these equations are functions, they can be graphed on a graphing
calculator.
Casio fx-7700GE:
gSR(?-
15.75
)-
2.5
⁄:gmS
R(?-
15.75
)-
2.5
e
TI-81:
Y‹R(|-
15.75
)-
2.5
ém
‹R(|-
15.75
)-
2.5
G
TI-82/83:
Y‹R([-
15.75
)-
2.5
é
m ‹ R ( [ -
15.75
)-
2.5
G
28
Quadratic Relations
● Casio fx-7700GE ● TI-81 ● TI-82/83
TI
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