Where can I find a proof of the quadratic formula?

Question

I need to show students how to prove it.

Answer 1

Solve the equation ax^2+bx+c=0 using the method of completing the square and prove it yourself.

ax^2+bx+c=o
ax^2+bx=-c
x^2+(b/a)x=-c/a
x^2+(b/a)x +(b/2a)^2=(b/2a)^2-c/a
(x+(b/2a))^2=(b^2)/(2a)^2-c/a
(x+(b/2a))^2=(b^2)/(4a^2)-(4ac)/(4a^2)
(x+(b/2a))^2=(b^2-4ac)/(4a^2)
Take the sqrt of both sides
x+(b/2a)=+_(sqrt(b^2)-4ac)/2a
x=(-b/2a)+_(sqrt(b^2)-4ac)/2a
x=(-b+_(sqrt(b^2)-4ac))/2a

Answer 2

It should be any book that has beginners chapters on quadratic equations. If you slept over you classes here is how to do it

(m+n)^2 = m^2 + 2mn + n^2. Keeping that in mind the objective it convert the general quardratic equation expression to a form
LHS^2 = RHS^2
This has two soln
LHS = +- RHS

ax^2 + bx + c = 0
Dividing by 4a

4a^2x^2 + 4abx + 4ac = 0
=> (2ax)^2 + 2(2ax)*(b) = 4ac
adding b^2 to both sides
=> (2ax)^2 + 2(2ax)*(b) + (b^2) = (b^2) - 4ac
=> (2ax)^2 + 2(2ax)*(b) + (b^2) = (b^2) - 4ac
=> (2ax+b)^2 = b^2 -4ac
=> 2ax + b = +/- sqrt(b^2 - 4ac)
=> 2ax = -b +/- sqrt(b^2 - 4ac)
=> x = -b/2a +/- sqrt(b^2 - 4ac)/2a

ie there are two roots of the equation
-b/2a - sqrt(b^2 - 4ac)/2a
-b/2a + sqrt(b^2 - 4ac)/2a

Answer 3

Dude, you just complete the square on a general quadratic equation ax^2+bx+c=0 where a is assumed to be non-zero.

First divide everything by a.
Subtract the constant c/a from both sides.
Take half of (b/a). Square it and add it to both sides.
Factor the left hand side into a perfect square.
Square root both sides.
Subtract -b/2a from both sides and simplify.
That's it!

Answer 4

It is in most algebra books. Just complete the square on the general quadratic: ax^2 + bx +c =0, where a not zero.

Answer 5

internet, the time you spent righting this question could have been the time spent to type quadratic formula prrof on yahoo, and you would have come up with the website below.

Answer 6

Give them an example of how the satellite uses its parabolic curve, and how the planetary movements move in a hyperbolic movement. Or just say, its simply math, live with it!