Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Completing the Square

Â· Remember there are three forms a parabola equation can have

y = ax 2 + bx + c

y = (x + h)(x + k)

y = a(x - h) 2 + k

Â· The first one is the standard form. It provides us no details about the location of  the vertex. We can use the value of a to determine the direction the parabola opens.

Â· The 2nd is in factored form. The equation could have been presented in 1st form and was factored. If we set this equation to zero (so that y = 0) we can use it find the roots (where the parabola crosses the x axis)

Â· The 3rd form is the vertex form of the parabola. It tells us the direction of the parabola (the value of a ) and the values of h and k tells the location of the vertex.

Â· The goal of completing the square is to go from the 1st form to the 3rd form, or the vertex form.

o The process is very mechanical

Â§ Arrange in descending powers y = ax 2 + bx + c

Â§ Factor the equation so the first term (the one with the power) has a coefficient of one

y = (ax 2 + bx) + c

Â§ Now the process really begins. Take half the middle term and add and subtract the square of that number.

Â· By doing so you have set up the equation for easier manipulation. You can see that we havenâ€™t changed the question, since we have added and subtracted the same number, we have in effect added zero.

Â§ We will now factor the first 3 terms, and move the 4th outside the brackets

Â§ This is the final product in a general form. It is to show you the

steps never change regardless of the coefficients!

word problems:

find the minimum product of 2 numbers whose difference is 8.

P = n(n-8) = n 2 - 8n Ã  complete the square to get P = (n-4) 2 -16. the number will be 4 and the product will be 16.