4g.+Quadratic+equations+&+discriminants

The quadratic equation can be used when the equation given is in standard form or can be put in standard form.
 * __How to solve Quadratic Equations __**

Standard form: ax2 + bx + c = 0 __Example 1:__ Step1: Place in standard form by subtracting 12x and adding 9. Step 2: Write out quadratic equation. Step 3: Substitute values of a,b,c in equation. Step 4: Simplify numbers under the fraction bar and the radical. Step 5: The square root of 0 = 0 so reduce 30/50. You end with 1 real solution of 3/5. 
 * Notice that a=25,b= - 30,c=9*
 * __For additional learning:__**

http://www.algebrahelp.com/lessons/equations/solvebyfactoring/ http://regentsprep.org/Regents/Math/faceq/LFacEq.htm

 __**What is a discriminant?**__ A discriminant in a quadratic equation determines the type and number of solutions. The discriminant is the value underneath the radical. Depending on the sign of the discriminant solutions will vary from 2 real solutions, 2 imaginary solutions or 1 real solution.

X > 0 Means that there are 2 Real Solutions. X = 0 Means that there are 1 Real Solution. X < 0 Means that there are 2 Imaginary Solutions.

__** How to predict number of solutions through the discriminant and solve? **__ __Example 2__: Step 1: Subtract 2 from both sides. Step 2: Write out the quadratic formula. Step 3: Substitute numbers for the variable a,b, and c. Step 4: Solve for the terms under the radical. Step 5: Simplify.
 * The discriminant is a positive number, so there should be two real solutions*

__Example 3__: Step 1:Write out quadratic equation & substitute. Step 2: Simplify and observe the discriminant. Step 3: Branch off and reduce.
 * The discriminant is equal to zero so there should be 1 real solution *

__Example 4__: Step1: Write out quadratic equation & substitute. Step 2: Simplify and observe the discriminant. Step 3: Simplify and reduce.
 * The discriminant is negative so there should be 2 imaginary solutions*

__ **For additional learning** __: http://hotmath.com/hotmath_help/topics/discriminant.html

__**Practice **__:

Guided practice to find the number of solutions use the following site: http://hotmath.com/tutor/?pid=genericalg2_5_6_QuadraticEquations_5_415

To find the value of the discriminant, and tell how many solutions there are. use the following site: http://hotmath.com/tutor/?pid=genericalg1_10_4_QuadraticEquations_5_915