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Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1
Chapter 9
Quadratic Equations and
Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2
Quadratic Equations and Functions
CHAPTER
9.1 The Square Root Principle and Completing the Square
9.2 Solving Quadratic Functions Using the Quadratic Formula
9.3 Solving Equations That Are Quadratic in Form
9.4 Graphing Quadratic Functions
99
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Solving Quadratic Equations Using the Quadratic Formula9.29.2
1. Solve quadratic equations using the quadratic formula.
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Using the Quadratic FormulaTo solve a quadratic equation in the form ax2 + bx + c = 0, where a 0, use the quadratic formula:
2 4
2
b b acx
a
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Example
Solve.
2 4
2
b b acx
a
22 7 3 0x x
Solution The equation is in the form ax2 + bx + c = 0, where a = 2, b = –7, and c = 3.
27 7 2 34
22x
7 49 24
4x
7 25
4x
7 5
4x
7 5
4x
7 5
4x
3x 1
2x
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ExampleSolve. 2 2 5 6x x
Solution First we need to write the equation in the form ax2 + bx + c = 0.
22 2 4 1 11
2 1x
2 4 44
2x
2 48
2x
2 2 11 0x x a = 1, b = –2, c = –11.
2 16 3
2x
2 4 3
2x
2 4 3
2 2x
1 2 3x
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ExampleSolve. 22 2 4x x
Solution First we need to write the equation in the form ax2 + bx + c = 0.
24 4 4 2 2
2 2x
4 16 4 2 2
2 2x
4 0
4x
22 4 2 0x x
1x
Notice that the radicand is 0, which causes this equation to have only one solution.
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Method When the Method is Beneficial
1. Factoring (Section 6.6) Use when the quadratic equation can be easily factored.
2. Square root principle (Section 9.1)
Use when the quadratic equation can be easily written in the form
3. Completing the square (Section 9.1)
Rarely the best method, but important for future topics.
4. Quadratic formula (Section 9.2)
Use when factoring is not easy, or possible, with integer coefficients.
Methods for Solving Quadratic Equations
2 2, or ( ) .ax c ax b c
