essential questions: what is the quadratic formula? why is it useful?
TRANSCRIPT
Essential Questions: What is the quadratic formula?
Why is it useful?
10-6: Using the Quadratic FormulaSometimes you’ll run into a quadratic
expression that cannot be factored.Example: x2 + 10x + 4 = 0
There is no combination of numbers that multiplies to get 4 and adds to 10.
Yet, there are real numbers that exist for x to make that a true statement.
There exists a formula that allows you to find the solutions for any quadratic equation, called the QUADRATIC FORMULA
10-6: Using the Quadratic FormulaA quadratic equation written in standard
formax2 + bx + c = 0
can be solved with the quadratic equation
2 4
2
b b acx
a
10-6: Using the Quadratic FormulaEmpirical verification that the formula works
x2 + 8x + 12 = 0 can be factored as(x + 6)(x + 2) = 0 meaningx = -6 OR x = -2
a = 1, b = 8, c = 122
2
4
2
4(1)(1(8) (8
2
8
(1)
16
28 4
2
2))
b b acx
a
8 4 42
2 28 4 12
62 2
x
x
10-6: Using the Quadratic FormulaUsing the quadratic formula to solve a
problem that can’t be factoredx2 + 10x + 4 = 0
a = 1, b = 10, c = 4
2
2 (1)((10) (1
4
2
4
2
10 84 10 9.17
2
40
1)
) )
2
(
b b acx
a
10 9.17 0.83
2 20.42
10 9.17 19.9.
2 259
17
x
x
10-6: Using the Quadratic FormulaAnother equation that can’t be factored
2x2 - 6x + 1 = 0a = 2, b = -6, c = 1
2
2
4
2
4
2
6 28 6 5.29
4 46 5.29 11.29
4 46 5.29 0.71
4
( 6) ( 6)
4
(1)(2)
(2)
2.82
0.18
b b acx
a
x
x
10-6: Using the Quadratic FormulaAssignment
Worksheet 10-6Problems 1 – 29, odds
Round answers to the nearest hundredth (2 decimal points)