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Solving Quadratic Equations
Using the Quadratic Formula
MATH 018
Combined Algebra
S. Rook
Overview
• Section 11.2 in the textbook:
– Solving quadratic equations using the
quadratic formula
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Solving Quadratic Equations
Using the Quadratic Formula
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Quadratic Formula
• We can solve an equation in
ax2 + bx + c = 0 format using the quadratic
formula
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 b  b  4ac
• Quadratic Formula: x 
2a
– ONLY uses numbers!
– ± indicates TWO solutions
– 2 ways to express the solution set
• Approximate – estimate the radical using a
calculator
• Exact – simplify the radical as far as possible
– This is the way we will use to express the
solution set
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Solving Equations Using the
Quadratic Formula
• One side MUST be set to 0
– Just like polynomial equations from section
6.6
• The quadratic formula uses ONLY
numbers!
– Just the coefficients, no variables
• The most common mistakes are sign
errors
– Watch your signs, especially under the
radical!
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Summary of Methods to Solve
Quadratic Equations
• Factoring: set one side equal to zero,
factor the remaining side, apply the Zero
Product Property
• Completing the Square: move the
constant over to the right side, ensure that
the coefficient in front of the squared term
is 1, complete the square, solve
• Quadratic formula: set one side equal to
zero, stick coefficients into the quadratic
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formula, simplify
Solving Quadratic Equations using
the Quadratic Formula (Example)
Ex 1: Solve using the quadratic formula:
a) x 2  4 x  1  0
d) 3x 2  6 x  1
b) x 2  5 x  7
c) 2 x 2  3  2 x
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Summary
• After studying these slides, you should
know how to do the following:
– Solve equations using the quadratic formula
• Additional Practice
– See the list of suggested problems for 11.2
• Next lesson
– Final Exam Review
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