andieje
asked on
completing the square of quadratic equation
Hi
If you have a quadratic iequation in the form ax^2 + bx + c = 0, I know how to complete the square to get the well-known formula which I won'r type out.
I have just read this and I don't understand how to complete the square in this different context:
for f(x) = ax^2 + bx + c we can complete the square on the right hand side and simplify to get....
I don't know how to complete teh square in this case. This is the only way i know how to do it:
ax^2 + bx + c = 0 --> take c to other side of equation
ax^2 + bx = -c ---> remove the coefficient of x^2
I won't go though all the steps but you get the picture. How do i complete the square in this case:
f(x) = ax^2 + bx + c
Perhaps if you show me the first few steps it will be obvious and I can complete the rest of it.
Thanks
If you have a quadratic iequation in the form ax^2 + bx + c = 0, I know how to complete the square to get the well-known formula which I won'r type out.
I have just read this and I don't understand how to complete the square in this different context:
for f(x) = ax^2 + bx + c we can complete the square on the right hand side and simplify to get....
I don't know how to complete teh square in this case. This is the only way i know how to do it:
ax^2 + bx + c = 0 --> take c to other side of equation
ax^2 + bx = -c ---> remove the coefficient of x^2
I won't go though all the steps but you get the picture. How do i complete the square in this case:
f(x) = ax^2 + bx + c
Perhaps if you show me the first few steps it will be obvious and I can complete the rest of it.
Thanks
I think you should complete the square to factor the expression rather than solve it.
The steps are essentially the same.
The Quadratic Formula give x = -b +/- sqrt(b² - 4ac)/2a
In this case you should wind up with something like
f(x) = ax^2 + bx + c = (x + b + sqrt(b² - 4ac)/2a) * (x + b - sqrt(b² - 4ac)/2a)
The steps are essentially the same.
The Quadratic Formula give x = -b +/- sqrt(b² - 4ac)/2a
In this case you should wind up with something like
f(x) = ax^2 + bx + c = (x + b + sqrt(b² - 4ac)/2a) * (x + b - sqrt(b² - 4ac)/2a)
ASKER
The answer is supposed to be
f(x) = (4ac - b^2)/4a + a(x + b/2a)^2
I'm not sure how it got that.
f(x) = (4ac - b^2)/4a + a(x + b/2a)^2
I'm not sure how it got that.
ASKER CERTIFIED SOLUTION
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I do not understand how the contexts are different? You just complete the square as usual on the RHS.
(4ac - b²/4a + a(x + b/2a)² is merely the completion of the square of ax² + bx + c ie that
ax² + bx + c = (4ac - b²/4a + a(x + b/2a)²
so that
if f(x)= ax² + bx + c
then f(x)= (4ac - b²/4a + a(x + b/2a)²
(4ac - b²/4a + a(x + b/2a)² is merely the completion of the square of ax² + bx + c ie that
ax² + bx + c = (4ac - b²/4a + a(x + b/2a)²
so that
if f(x)= ax² + bx + c
then f(x)= (4ac - b²/4a + a(x + b/2a)²
SOLUTION
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ASKER
Can i do this then as the first step:
f(x)= ax² + bx
f(x) - c = ax^2 + bx
I'm not that comfortable with function notation. Not used it for years. I guess its valid to write f(x) - c?
How do you get the sqaured notation glynweb? f(x)= ax² + bx
I ahve to type ^2
f(x)= ax² + bx
f(x) - c = ax^2 + bx
I'm not that comfortable with function notation. Not used it for years. I guess its valid to write f(x) - c?
How do you get the sqaured notation glynweb? f(x)= ax² + bx
I ahve to type ^2
ASKER
sorry, of course its the same. It looked completely different on first glance but if you work it through its the same. I also thought it had to equal 0 for you to do this.
thanks
thanks
http://www.occc.edu/maustin/Quadratic_Functions/Quadratic%20Functions.htm