Quadratic Equations and
Problem Solving
MATH 018
Combined Algebra
S. Rook
Overview
• Section 6.7 in the textbook:
– Solving Quadratic word problems
– Applying the Pythagorean Theorem
2
Solving Quadratic Word
Problems
3
Solving Quadratic Word
Problems
• Object is to extract a quadratic equation
from the word problem
• Solve by factoring
• Takes practice
4
Solving Quadratic Word
Problems (Example)
Ex 1: Set up a quadratic equation and
solve:
a) The difference of the square of a number and
the number itself is thirty
b) The sum of four times the square of a number
and eight times the number itself is negative three
c) Two consecutive odd integers whose product is
63
5
Applying the Pythagorean
Theorem
Applying the Pythagorean
Theorem
• Pythagorean Theorem: given a right triangle
with legs a & b and hypotenuse c, the following
relationship exists: a2 + b2 = c2
– It does not matter which
of the legs is a and which
is b
– The hypotenuse, c, is the
longest side AND is
ALWAYS opposite the 90°-angle
• When solving problems with right triangles, it is
often helpful to draw a picture
7
Applying the Pythagorean
Theorem (Continued)
• Bear in mind the domain of the problem
(i.e. what the problem is addressing)
– Even though some solutions of an equation
may be mathematically correct, they may not
make sense in the context of the problem
• What is the domain of the Pythagorean
Theorem?
– What do you know sign-wise about the
domain?
8
Applying the Pythagorean
Theorem (Example)
Ex 2: A 10 foot ladder is leaning on a
building which is perpendicular to the
ground where the top of the ladder
(vertically) extends two feet more than
across the ground (horizontally). Set up an
equation and find how many feet the
ladder extends off the ground (vertically)
9
Applying the Pythagorean
Theorem (Example)
Ex 3: One leg of a right triangle is 4
millimeters longer than the smaller leg and
the hypotenuse is 8 millimeters longer
than the smaller leg. Find the lengths of
the sides of this triangle
10
Summary
• After studying these slides, you should
know how to do the following:
– Solve quadratic word problems
– Solve problems involving the Pythagorean
Theorem
• Additional Practice
– See the list of suggested problems for 6.7
• Next lesson
– Simplifying Rational Expressions (Section 7.1)
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