Equations By Design
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Challenge:
Create a recognizable picture using only
the following types of equations:
Linear,
Quadratic, Polynomial, Logarithmic, Exponential, Square Root, Absolute Value,
Sinusoidal
The picture must be made using at least four different types
of equations. A program must be designed on a graphics calculator to set
up the graphing window and to draw the equations/picture.
Solution:
Graphs can be transformed by
stretching, by shifting, and by reflection by adding key operations to their
equation. The level of the effect of
the transformation is determined by the value of the number entered with those
operations.
All
transformed equations have this general format:
Y = A(B(X-h))+k
The
value of “A” can stretch the graph vertically and/or flip the graph upside-down
The
value of “B” can stretch the graph horizontally and/or flip the graph
left-to-right
The
value of “h” will shift the graph left or right
The
value of “k” will shift the graph up or down
To
only graph part of an equation, limitations are put onto the equation so it
only will graph for specific values of x. For example,
Y= (-3(2(x-4)2 +
7))/((x>4)(x<10))
Reading
across, this quadratic equation would be flipped upside down and vertically
stretched by 3 (A=-3), horizontally stretched by ½ (B=2), shifted right 4
(h=4), shifted up 7 (k=7), and graph only for values of x from 4 to 10.
Equations By Design Directions
Downloadable Picture Programs
More Information on Transforming Equations
Back to
Equations Exhibits Page