Download TI Graphing 2.6 #30, #22

Additional Solving Subtleties
From §2.6 using the TI–84+
3
§2.6 # 30; Confirm algebraic solution graphically: x  5x2  9 ; Algebraic Solution: x   i
2
Big Idea: Only real solutions will show when graphed on the TI–84+. Imaginary solutions will
not be visible on the graph, since we are graphing in the Real Number System.
Using Technique 1. Screen shot
from older OS.
Using Technique 1. Screen shot
from newer OS.
Y1 and Y2 graphed in Standard
Zoom.
Note: When entering a square root,
the calculator will give you the
starting parenthesis and you will
have to enter the ending
parenthesis.
Note: No parenthesis needed. Just
right arrow out from under the
square root.
No intersection points, means NO
REAL SOLUTIONS. Only
Imaginary Solutions, if any.
3
Algebraically we got: x   i . That
2
is we have algebraically, we have only
imaginary solutions.
Using Technique 2. Screen shot
from older OS.
Note: When entering a square root,
the calculator will give you the
starting parenthesis and you will
have to enter the ending
parenthesis.
Using Technique 2. Screen shot
from newer OS.
Note: No parenthesis needed. Just
right arrow out from under the
square root.
Math 114 – Additional Solving Subtleties 2.6 on TI–84+
Y3 graphed in Standard Zoom.
NO x–intercepts means no real
roots, that is, no real solutions of
our original equation. Only
Imaginary Solutions, if any.
3
Algebraically we got: x   i .
2
That is we have algebraically, we
have only imaginary solutions.
Page 1 of 2
§2.6 # 22; Confirm algebraic solution graphically: 10 x  1  8  0 ; Algebraic Solution: No Solution
Big Idea: Using Technique 2, “No Solution” means “No x–intercepts.”
Here we illustrate only Technique 2 Using Technique 2. Screen shot
since the equation is already set
from newer OS.
equal to 0. This screen shot is from
the older OS.
Y1 graphed in Standard Zoom.
The majority of the graph is not
visible, but we picked up a piece of
it at the top of the y–axis that
appears to be around the point
(0, 9). In reality this is our y–
intercept.
To verify a y–intercept of (0, 9)…
Let x = 0, then simplify to get a
y–value of 9 for y1.
Since we picked up only a small
piece of the graph, let’s change the
viewing rectangle to go higher on
the y–axis. Using your grey
WINDOW button, make the
following change to Standard
Zoom. Arrow down, and change
the Ymax value. Set Ymax = 20.
Then hit GRAPH.
This is the upper half of a parabola opening to the right, with a
y–intercept of (0, 9). There are NO x–intercepts, so we have NO real
solutions.
Looking only at the graph, and not at the algebra, it is possible that we
might have complex conjugate imaginary solutions that we can’t see
graphically, but algebraically we got back No Solution (No Real Solution
AND No Imaginary Solution) which is consistent with this graph.
Math 114 – Additional Solving Subtleties 2.6 on TI–84+
Page 2 of 2