Greenwood press

Vectors for applications in many dimensions.)
online sources for further exploration
Astronomy connections

88
PYTHAGOREAN THEOREM
A cross-sectional view of earth that
illustrates the viewing distance from
a lighthouse to the horizon. Note that
the diagram is not drawn to scale.

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Baseball and the Pythagorean Theorem


Construction

Latitude and longitude

Real-world applications

When would I use the Pythagorean Theorem?

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QUADRATIC FUNCTIONS
Quadratic functions take on the standard form 
f (x) = ax
2
+ bx + c, and
have graphs that are parabolas. Applications of quadratic functions commonly
refer to maximizing or minimizing a quantity, because they will have a highest or
lowest point at their vertex. For example, a business owner would be interested in
the greatest profit his or her company can attain based on the sales of its products.
This maximum or minimum point can be found by rewriting the expression
into vertex form through a process called completing the square. The vertex form
of a quadratic function is 
f (x) = a(x
− h)
2
+ k, where (h, k) is the vertex. The
following symbolic manipulation illustrates how the standard form 
f (x) =
ax
2
+ bx + c can be manipulated into vertex form. Factor the leading coeffi-
cient,
a, from the first two terms: f (x) = a(x
2
+
b
a
x) + c. Complete the square 
of the factored component, and then subtract that value so that nothing is added
to the expression:
f (x) = a(x
2
+
b
a
x +
b
2
4a
2
) −
ab
2
4a
2
+ c.