PreCalculus Class Notes QF8 Solve Problems with Quadratic Equations
GSP Vertical Team: Cutout Box
Example: A box is being constructed by cutting 2-inch squares from the corners of a rectangular
piece of cardboard that is 6 inches longer than it is wide. If the box is to have a volume of 224
cubic inches, find the dimensions of the piece of cardboard.
Solution: Label the dimensions of the box in terms of x, the width of the cardboard. Write an
equation for the volume and solve for x. Then state the dimensions of the cardboard.
Projectile Motion
General Formula for Path of an Object with Gravity
s ( t ) = −16t 2 + v0t + s0
where
s(t) is the height (feet) of the object at time, t (seconds).
v0 is the initial vertical velocity (ft per sec).
Positive velocity if object is thrown up and negative velocity if the object is thrown down.
s0 is the initial height (feet) of the object.
Example: The table shows the height of a projectile shot into the air.
t (sec)
0
2
4
6
8
s(t) (ft)
96
400
576
624
544
(a) Use s ( t ) = −16t 2 + v0t + s0 to model the data.
(b) After how many seconds did the projectile strike the ground?
Geometry Application
Set Up Homework #111
A window comprises a square with sides of length x and a semicircle with diameter x, as shown.
If the total area of the window is 463 square inches, estimate the value of x to the nearest
hundredth.