TI 84 Calculator: Part II

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TI 84 Calculator Part II

• Macon State College
• Mary Dwyer Wolfe, Ph.D.
• Gaston Brouwer, Ph.D.
• July 2009
• http//calculator.maconstate.edu

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TI 84 Calculator

• Solving equations using the Intersection of
  Graphs Method
• Scatterplots and Line Graphs
• Linear Regression
• Applications
• Quadratic Equations and the Vertex
• Maximum/Minimum Applications

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Solving by the Intersections of Graphs Method
The Intersections of Graphs method of solving
equations is an alternate method of solving
equations (not a replacement method). This
method sometimes leads to approximate solutions
whereas traditional symbolic methods can usually
produce exact solutions. The Intersections of
Graphs method is particularly useful when
symbolic solutions are not possible.
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Solving by the Intersections of Graphs Method

• Step 1 Enter the left side of the equation for
  Y1 and the right side of the equation for Y2
  (Under Y)
• Step 2 Graph the equations in a window where the
  Intersection is visible.
• Step 3 Compute the Intersection (2nd CALC 5)
• Step 4 The x coordinate of the intersection
  point is the solution to the equation

Solve 2 (3x 5) 8x 17
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Solving by the Intersections of Graphs Method
Solve 2 (3x 5) 8x 17
Step 1
Step 2
Step 3
Step 3 continued
Step 4 The solution is approximately x
-1.818182 or x -1.82 to the nearest hundredth
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Solving by the Intersections of Graphs Method

• Try this one Solve 2x2 5x 12

x -1.5 or x 4
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Solving by the Intersections of Graphs Method

• Try this one

Solve ex2 52x for x
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Solving a Linear Inequality Graphically Example
1

• Solve

? 2, 15, 1 by ? 2, 15, 1
S T E P 1
S T E P 2
First we find the intersection of the left and
right side just as we do with equations. Note
that the graphs intersect at the point (8.20,
7.59). Since this is an inequality, we must now
determine if the correct sign is gt or it flips to
lt.
S T E P 3
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Solving a Linear Inequality Graphically Example
1 -- continued

• Solve

Y1
Y2
S T E P 4
Note that the graphs intersect at the point
(8.20, 7.59). So we center an x-value of 8. When
x lt 8.20, Y1 lt Y2, but when x gt 8.20, Y1 gt
Y2. Since our original equation was Y1 gt Y2 , we
know x gt 8.20. Thus in interval notation the
solution set is (8.20, 8).
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Solving a Linear Inequality Graphically Example
2

• Solve

?10, 10, 1 by ?10, 10, 1
S T E P 1
S T E P 2
Note that the graphs intersect at the point
(?1.36, 2.72). Since this is an inequality, we
must now determine if the correct sign is gt or it
flips to lt.
S T E P 3
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Solving a Linear Inequality Graphically Example
2

• Solve

Y1
Y2
S T E P 4
Note that the graphs intersect at the point
(?1.36, 2.72). We find that x ?1.36 when Y1
gt Y2. Thus in interval notation the solution set
is (? 8, ?1.36.
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Solving Compound Inequalities

• Example Suppose the Fahrenheit temperature x
  miles
• above the ground level is given by T(x) 88
  32 x.
• Determine the altitudes where the air temp is
  from 300 to 400.
• We must solve the inequality
• 30 lt 88 32 x lt 40
• Graph all three parts in the same window

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Solving Compound Inequalities

• We must solve the inequality -- continued
• 30 lt 88 32 x lt 40
• Find the 2 intersection points

Note Use the down arrow to switch to the 2nd two
equations.
Symbolically, Between 1.5 and 1.8125 miles above
ground level, the air temperature is between 30
and 40 degrees Fahrenheit.
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Scatterplots and Line Graphs

• Graph the set of data

x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
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Scatterplots and Line Graphs
x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
Scatterplot
Line Graph
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Least Squares Regression (Line of Best Fit)

• Note that this data appears to be linear

x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
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Least Squares Regression (Line of Best Fit)
x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
f(x) 2x - 3
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Least Squares Regression (Line of Best Fit)
x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
Using this regression equation, f(x) 2x - 3,
what y (or f(x)) is paired with x 10?
That is, find f(10).
f(10) 17
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Least Squares Regression (Line of Best Fit)
x 1 2 3 4 5 6 7
y -1 1 3 5 7 9 11
Using this regression equation, f(x) 2x - 3,
what x is paired with y f(x) 10?
That is, solve 10 2x - 3.
x 6.5 is paired with y 10
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More Linear Regression

• Find the equation of the line that passes
  through the points (2, -3) and (-5, -4).

We could use point-slope form and find the
equation symbolically or
We could use linear regression.
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Nearly Linear Data An Application
From NCTM.org
Predict the maximum height for a bike that weighs
21.5 pounds if all other factors are held
constant.
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Nearly Linear Data An Application
Predict the maximum height for a bike that weighs
21.5 pounds if all other factors are held
constant.
A height of 9.994 inches is expected for a weight
of 21.5 pounds.
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Nearly Linear Data An Application
Your turn! You already have the model in your
calculator!
Predict the maximum weight for a bike that so
that it can reach a height of 10.5 inches if all
other factors are held constant.
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Nearly Linear Data An Application
Predict the maximum weight for a bike that so
that it can reach a height of 10.5 inches if all
other factors are held constant.
A weight of about 18.3 pounds is expected for a
height of 10.5 inches.
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Finding a Vertex (Max/Min Point)

• Find the vertex of y 2x2 7x - 1

The vertex is approximately (1.75, -7.125)
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Find the Vertex
Your Turn!
Find the vertex of y -3x2 5x - 4
The vertex is approximately (0.833, -1.912)
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Application Find a Maximum
A home owner has 200 feet of fencing to make a
rectangular garden in his yard that is protected
from the rabbits and deer. He decides to use the
long side of the house as one side of the fenced
area so a larger area can be obtained as less
fencing is needed. That way he can walk out the
back door into the garden. What of the
dimensions of garden that maximize the area for
planting?
200 2x
x
x
The house!
A(x) x(200 2x)
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Application Find a Maximum
A(x) x(200 2x)
X 50 200 2x 200 2(50) 100 The
dimensions are 50 by 100 feet.