Lesson Completeing the Square and Quadratic Equation (how to find and use it)

Algebra ->  Quadratic Equations and Parabolas -> Lesson Completeing the Square and Quadratic Equation (how to find and use it)      Log On


   

This Lesson (Completeing the Square and Quadratic Equation (how to find and use it)) was created by by Nate(3500) About Me : View Source, Show
About Nate:
Firstly, let us discover: Completeing the Square
Ex.) x^2 + 2x + 1 = 0
x^2 + 2x = -1 leave all the x-terms on one side
(x + 1)^2 = -1 sum half of the linear term to x squared
(x + 1)^2 = 1 - 1 sum 1%5E2 with the other term on the other side of the equation
(x + 1)^2 = 0
x + 1 = 0
x = -1
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B2x%2B1%2C0%29
Lets try a harder one now:
Ex.) 2x^2 + 6x + 4 = 0
2x^2 + 6x = -4
x^2 + 3x = -2 divide everything by two to get your leading coefficient to be positive one
(x + 3/2)^2 = 9/4 - 2 = 9/4 - 8/4 = 1/4
x + 3/2 = +- 1/2
x = -3/2 +- 1/2
x = -2 and x = -1
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C2x%5E2%2B6x%2B4%2C0%29
Now, the quadratic formula:
ax%5E2+%2B+bx+%2B+c+=+0
ax%5E2+%2B+bx+=+-c
x%5E2+%2B+bx%2Fa+=+-c%2Fa

x+%2B+b%2F2a = +- sqrt%28b%5E2+-+4ac%29%2F%282a%29
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
How to use it:
Ex.) 3x^2 + 7x + 2 = 0
Remember: ax^2 + bx + c = 0
a=3 and b=7 and c=2
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
x+=+%28-7+%2B-+sqrt%287%5E2+-+4%2A3%2A2%29%29%2F%286%29
x+=+%28-7+%2B-+sqrt%2849+-+24%29%29%2F%286%29
x+=+%28-7+%2B-+sqrt%2825%29%29%2F%286%29
x+=+%28-7+%2B-+5%29%2F%286%29
x+=+-2 and x+=+-1%2F3
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C3x%5E2%2B7x%2B2%2C0%29
This lesson has been accessed 10302 times.