Texas Instruments (TI) Calculators for Functions



Samuel Dominic Chukwuemeka (SamDom For Peace) You may use any of these TI calculators:
TI-83 Plus
TI-84 Plus series
TI-Nspire CX series
TI-89 Titanium
TI-73 Explorer

The first thing we need to do is to reset the Random Access Memory (RAM).
This will clear everything that was initially stored by a previous user.
Also, after each problem, it is recommended that you reset the calculator.


Reset the Calculator
(1.) Reset 1

(2.) Reset 2

(3.) Reset 3

(4.) Reset 4



Set up the Calculator
The first thing we need to do is to turn Diagonstic On

(1.) Set Up 1

(2.) Set Up 2

(3.) Set Up 3

Let us do some examples.
NOTE: Please begin from the first example. Do not skip.



Concept: Graphing Quadratic Functions
(1.) A golf ball is hit with an initial velocity of 170 feet per second at an inclination of 45° to the horizontal.
In​ physics, it is established that the height h of the golf ball is given by the function

$ h(x) = \dfrac{-32x^2}{170^2} + x \\[5ex] $ where x is the horizontal distance that the golf ball has traveled.

(a.) Determine the height of the golf ball after it has traveled 100 feet.

(b.) What is the height after it has traveled 200 ​feet?

(c.) What is h(400)​?
Interpret this value.

(d.) How far was the golf ball​ hit?

(e.) Use a graphing utility to graph the function $h = h(x)$
[0, 1000] by [0, 240], Xscl = 100, Yscl = 20

(f.) Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 80 feet.

(g.) Create a TABLE with TblStart = 0 and Δ Tbl = 25
To the nearest 25​ feet, how far does the ball travel before it reaches a maximum​ height?

(h.) What is the maximum​ height?

(i.) Adjust the value of ΔTbl until you determine the​ distance, to within 1​ foot, that the ball travels before it reaches a maximum height.

Number 1 set-up 1

Number 1 set-up 2

Number 1 set-up 3

Number 1 set-up 4

(a.), (b.), (c.):
Numbers 1a, 1b, 1c

Numbers 1a, 1b, 1c: Decimals

Rounding to two decimal places:

$ (a.)\;\;h(100) \approx 88.93\;feet \\[3ex] (b.)\;\;h(200) \approx 155.71\;feet \\[3ex] (c.)\;\;h(350) \approx 214.36\;feet \\[3ex] $ (a.) The height of the golf ball after it has traveled a horizontal distance of 100 feet is approximately 88.93 feet.
(b.) The height of the golf ball after it has traveled a horizontal distance of 200 feet is approximately 155.71 feet.
(c.) The height of the golf ball after it has traveled a horizontal distance of 350 feet is approximately 214.36 feet.

$ (d.) \\[3ex] h(x) = 0 \\[3ex] h(x) = \dfrac{-32x^2}{170^2} + x \\[5ex] \implies \\[3ex] 0 = \dfrac{-32x^2}{28900} + x \\[5ex] \dfrac{-32x^2}{28900} + x = 0 \\[5ex] \dfrac{-32x^2}{28900} + \dfrac{28900x}{28900} = 0 \\[5ex] \dfrac{-32x^2 + 28900x}{28900} = 0 \\[5ex] 28900\left(\dfrac{-32x^2 + 28900x}{28900}\right) = 28900(0) \\[5ex] -32x^2 + 28900x = 0 \\[3ex] x(-32x + 28900) = 0 \\[3ex] x = 0 \;\;\;or\;\;\; -32x + 28900 = 0 \\[3ex] x = 0 \;\;\;or\;\;\; -32x = -28900 \\[3ex] x = 0 \;\;\;or\;\;\; x = \dfrac{-28900}{-32} \\[5ex] x = 0 \;\;\;or\;\;\; x = 903.125 \\[3ex] $ [0, 1000] by [0, 240], Xscl = 100, Yscl = 20
X = [0, 1000]
Y [0, 240]
Number 1 set-up 5

(e.)
Number 1e

Number 1 set-up 6

Number 1 set-up 7

Number 1 set-up 8

Number 1 set-up 9

Number 1 set-up 10

Number 1 set-up 11

(f.) Part 1:
Number 1f-1

Do the process: 5: intersect again.

Number 1 set-up 8

Number 1 set-up 12

Number 1 set-up 13

Number 1 set-up 14

(f.) Part 2:
Number 1f-2

The ball has traveled approximately 88.71 feet and 814.41 feet when the height of the ball is 80 feet.

Let us convert the values in the function to display decimal values of the output

$ h(x) = \dfrac{-32x^2}{170^2} + x \\[5ex] h(x) = -0.0011072664x^2 + x \\[3ex] $ Number 1 set-up 15

Number 1 set-up 16

Number 1 set-up 17

Numbers 1g-1h

(g.), (h.)
To the nearest 25 feet:
The ball travels 450 feet before it reaches the maximum height of 225.778554 feet (apprxoimately 225.78 feet when rounded to two decimal places).

Number 1 set-up 18

Numbers 1i

(i.) To the nearest 1 foot:
The ball travels 452 feet before it reaches the maximum height of 225.77810454144 feet.




Concept:
(a.)

(2.)






Concept:
(3.)





Concept:
(4.)





(5.)





(6.)