# How do you find the minimum?(Quadratics)

• October 16th 2007, 05:50 AM
Kagome
How do you find the minimum?(Quadratics)
Hi,
I'm in Grade Twelve Academic Math and I need to know how to find the minimum of any given problem.
PLEASE PUT DOWN STEPS to finding the minimum, not just writing a question then jumping to the answer.
I would really appreciate the help.
• October 16th 2007, 06:49 AM
topsquark
Quote:

Originally Posted by Kagome
Hi,
I'm in Grade Twelve Academic Math and I need to know how to find the minimum of any given problem.
PLEASE PUT DOWN STEPS to finding the minimum, not just writing a question then jumping to the answer.
I would really appreciate the help.

You want to know how to find the minimum value of the function
$y = ax^2 + bx + c$
where a is a positive number.

Can you use Calculus or not?

-Dan
• October 16th 2007, 08:31 AM
Kagome
Math help
I don't think so, I'm not great at math yet I'm in academic math(not basic).
• October 16th 2007, 08:35 AM
Jhevon
Quote:

Originally Posted by Kagome
I don't think so, I'm not great at math yet I'm in academic math(not basic).

well, there are several ways of doing this. the two most prominent ways are to: (1) complete the square, or (2) use the vertex formula.

note that only quadratics where the coefficient of x^2 is positive have a minimum value, and it occurs at their vertex. post a specific question if you want to see these methods demonstrated
• October 16th 2007, 11:50 AM
SnipedYou
It should be $(\frac{-b}{2a},$ the value of x put into the original equation) right?
• October 16th 2007, 12:23 PM
Jhevon
Quote:

Originally Posted by SnipedYou
It should be $(\frac{-b}{2a},$ the value of x put into the original equation) right?

yes, $x = \frac {-b}{2a}$ gives the x-value for the vertex in any quadratic in x. (of the form $y = ax^2 + bx + c$)