Proving the Quadratic Formula (2.5.1) Flashcards
• Completing the square for a generalized quadratic equation gives us a very powerful formula for solving all quadratic equations.
• Completing the square for a generalized quadratic equation gives us a very powerful formula for solving all quadratic equations.
Begin with a generalized equation, one that is solving for x and using letters rather than specific numbers in each position.
Step one in completing the square is to divide the entire
equation by any coefficient of x^2 other than 1, in this case, a.
Next step is to move the constant, in this case c/a to the right side of the equation.
Now for the biggie. Divide the coefficient of x by 2:
(b/a) ÷ 2 = b/2a.
Then square the number: b^2/4a^2.
Next add that squared number to both sides of the equation.
Write the left side as the square of a binomial.
Take the square root of both sides.
Finally, move the constant on the left side to the right side and you have your two final answers. Remember also to rationalize the denominator.
You rarely have to develop the quadratic formula in this
fashion. However, you will use it frequently.
Begin with a generalized equation, one that is solving for x and using letters rather than specific numbers in each position.
Step one in completing the square is to divide the entire
equation by any coefficient of x^2 other than 1, in this case, a.
Next step is to move the constant, in this case c/a to the right side of the equation.
Now for the biggie. Divide the coefficient of x by 2:
(b/a) ÷ 2 = b/2a.
Then square the number: b^2/4a^2.
Next add that squared number to both sides of the equation.
Write the left side as the square of a binomial.
Take the square root of both sides.
Finally, move the constant on the left side to the right side and you have your two final answers. Remember also to rationalize the denominator.
You rarely have to develop the quadratic formula in this
fashion. However, you will use it frequently.
x=(-b+/-(sqrt b^2 - 4ac))/2a
x=(-b+/-(sqrt b^2 - 4ac))/2a
