4.6 Solving Quadratic Equations by Using the Quadratic Formula
We could use completing the square to show the development of the quadratic formula, but this serves
no real purpose. If you are interested it is on page 362 of your text and you are welcome to look over it.
Fact: The solutions to ax 2  bx  c  0 are given by the quadratic formula: x 
Steps to Solving Quadratic Equations Using the Quadratic Formula:
1.
2.
3.
4.
5.
Set the quadratic equal to zero.
Put the quadratic in standard form.
Substitute values for a, b, and c into the quadratic formula.
Simplify the quadratic formula – radical first, then fraction last.
Check answers in the original equation.
Examples: Solve using the formula.
1. 4 x 2  3x  10  0
2. 2h2  7h  9
b  b 2  4ac
.
2a
3. 2 x2  13x  15  0
4. 1.5x2  2  6.5x
5. 2.6 x2  3.8x  4.2  0
You try them examples: Solve using the square root property, factoring, or the quadratic formula.
1.
4 x3  5 x 2  6 x  0
2.
6 p 2  15  21
3.
k 2  6k  5
4. 1.3x2  4.1x  7.2  0
Homework: 1 – 10 all, 23 – 67 odd