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50 Activities
Note: An alternative for solving equations for real numbers is to use the
built-in Equation Solver.
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 × 12.5 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.
6. Press y [ repeatedly until this
quadratic-formula expression is displayed:
7. Press Í to find the other solution for
the quadratic equation: 2x
2
N x+3=0.
1. Press o to display the
Y= editor, which is
where you define functions for tables and
graphing.
2. Press £
20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹
„ ¤ „ Í to define the volume
function as
Y1 in terms of X.
„ lets you enter X quickly, without
having to press ƒ. The highlighted
=
sign indicates that
Y1 is selected.
b– b
2
4ac–+
2a
---------------------------------------
Begin by defining a function that describes
the volume of the box.
From the diagram:
2X + A = 20
2X + 2B = 25
V = A…B…X
Substituting:
V = (20 N 2X) (25à2 N X) X
X
A
X
BX
B
20
25