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EGR 1101 Unit 2
Quadratic Equations in Engineering
(Chapter 2 of Rattan/Klingbeil text)
Mathematical Review

In linear equations, which we studied
last time, the two variables (x and y) are
both raised to the first power:
y  5 x  10

In a quadratic equation, the dependent
variable is raised to the first power and
the independent variable is raised to
the second power. For example:
y  2 x  3x  10
2
Graphical Interpretation

The graph of a quadratic equation is a
parabola. In MATLAB:
> fplot('2*x^2 + 3*x + 10', [-10, 10])
Two Common Questions Involving
Quadratic Equations
1.
2.
Given a quadratic equation, find the value
of y for a particular value of x. (Easy!)
Given a quadratic equation, find the value
of x for a particular value of y. (Harder!)
Three Methods

1.
2.
3.
We’ll study three ways to answer the
second type of question:
Factoring
Quadratic formula
Completing the square
Today’s Examples
1.
2.
3.
Height of a projectile
Power and current in a circuit
Resistors in parallel
Some Symbols Used in Electrical
Drawings

Resistor:

Voltage Source:

Lamp (light bulb):

Circuit containing these
three components:
Three Basic Electrical Laws

Kirchhoff’s Voltage Law (KVL): Around
any closed loop in a circuit, the sum of the
voltage rises is equal to the sum of the
voltage drops.
•
Ohm’s Law: For a resistor, voltage equals
current times resistance:
V = IR
•
Power Law: For any component, power
equals current times voltage:
P = IV
Resistors in Series or Parallel

If two resistors are connected in series
(end-to-end), total resistance is the sum of
the two resistances:

If two resistors are connected in parallel
(connected at both ends), total resistance is
given by the product-over-sum rule: