ALGEBRA CHAPTER 9 SECTION 9-6: THE QUADRATIC FORMULA AND THE DISCRIMINANT OBJECTIVE:

1)

solve quadratic equations by using the quadratic formula use the discriminant to determine the number of solutions for a quadratic equation

You can solve the standard form of quadratic equation ax2 + bx + c = 0 for x. The results is called the Quadratic Formula.

2)

Use the Quadratic Formula to solve: x2 - 2x - 24 = 0 a=

3)

b=

c=

Use the Quadratic Formula to solve: 24x2 - 14x = 6 a=

b=

c=

4)

5)

Solving Quadratic Equations Method

Can be used

Comments

graphing

always

Not always exact: used only when an approximate solution is sufficient

factoring

sometimes

Use if constant term is 0 or factors are easily determined

completing the square

always

Use for equations of the form x2 + bx + c = 0, where b is an even number

Quadratic Equations

always

Other methods may be easier to use in some cases, but this method always give an accurate solutions

use square root

sometimes

Only if b = 0

In the Quadratic Formula, the expression under the radical sign, b2 - 4ac, is called the discriminant. The value of the discriminant can be used to determine the number of real roots for a quadratic equation. (what happens to the number under the radical sign in each case?)

If the value is greater then 0, then there will be 2 roots. If the value is less then 0, then there will be 0 root. If the value is equal to 0, the there will be 1 root

6)

State the value of the discriminant for each equation. Then determine the number of real roots of the equation. a)

2x2 + 10x + 11 = 0

b) 4t2 - 20t + 25 = 0

c) 3m2 + 4m = - 2

HW: page 586 - 588: 7 - 33 odd, 35 - 49, 55 - 61