Operation Manual

Chapter 17: Activities 297
Box with Lid
Defining a Function
Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12½ cm
rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a
lid. What value of X would give your box the maximum volume V? Use the table and graphs to
determine the solution.
3. Press 2 ¿ ƒ A ƒ [:] Ì 6 ¿
ƒ
B ƒ [:] 5 ¿ ƒ C Í.
The coefficient of the x
2
term, the
coefficient of the X term, and the constant
for the new equation are stored to A, B,
and C, respectively.
4. Enter the quadratic formula using Classic
entry: £ Ì ƒ
B Ã y C ƒ B ¡ ¹
4 ƒ A ƒ C ~ ¤ ¥ £ 2 ƒ A ¤.
Because the solution is a complex number,
you have to enter the formula using the
division operation instead of using the
n/d
shortcut template. Complex numbers are
not valid in the n/d template in input or
output and will cause Error: Data Type to
display.
5. Press Í to find one solution for the
equation 2x
2
N 6x + 5 = 0.
6. Press }
to highlight the quadratic-formula
expression, and then press Í to paste it
to the entry line.
7. Press | until the cursor is on the
+ sign in
the formula. Press ¹ to edit the quadratic-
formula expression to become
.
8. Press Í to find the other solution for
the quadratic equation: 2x
2
N 6x + 5 = 0.
9. Change the solution to  1:FRAC as
needed.
Note: To convert complex numbers to fraction
or decimal forms, use  1:FRAC or 
2:DEC. ƒ ^ 4: 4F3 4D can be used for
real numbers only.