Alg1, Unit 15, Lesson03_absent-student, page 1
Solving equations using the Quadratic Formula
A polynomial of degree two is a quadratic. The general form of the
quadratic equation is:
ax2 + bx + c = 0
where a, b, and c are constants
There are two solutions to this quadratic equation. They are given by
the quadratic formula:
− ± √ − =
(Roots produced by the quadratic formula are exactly the same as
those produced by factoring.)
Example 1: Find the roots of this quadratic polynomial: x2 + 2x – 15
Example 2: Solve x2 + 10x + 24 = 0
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Alg1, Unit 15, Lesson03_absent-student, page 2
Example 3: Find the zeros of 2x2 + 3x – 2.
See Enrichment Topic G for a derivation of the Quadratic Formula.
Enrichment Topic H presents the technique of “completing the square.”
The derivation of the quadratic formula in Enrichment Topic G uses this
technique of solving a quadratic equation.
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Alg1, Unit 15, Lesson03_absent-student, page 3
Assignment: Use the quadratic formula in solving these problems.
1. Solve x2 + 13x + 42 = 0
2. Find the roots of x2 + 8x – 9
3. Find the zeros of 2x2 – 3x + 1
4. Solve x2 – 6x – 27 = 0
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Alg1, Unit 15, Lesson03_absent-student, page 4
5. Solve -x2 + 3x – 2 = 0
6. Solve 10x2 – 9x – 7 = 0
7. Solve -x2 + x + 30 = 0
8. What are the roots of 3x2 + x – 14?
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Alg1, Unit 15, Lesson03_absent-student, page 5
9. What are the zeros of 6x2 – 17x + 12 = 0?
10. Solve 6x2 + 7x + 2 = 0.
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