-b/2a is not working for me

[nolsen01]

In precalculus, we are learning to find the minimum or maximum of a quadratic equation.

A "trick" they gave us was x = -b/2a for ax^2+bx+c where a =/= 0.

-b/2a is supposed to be a shortcut for finding the maximum or minumum of a quadratic function but it is not working for me. Here is an example:

T=2b^2-12b+36

When I change it into standard for, I get 2(b-3)^2 + 18 which would suggest that the minimum is 18. However, when I apply the formula above, I get:

-(-12) / 2(2) = 12 / 4 = 3.

This is the second time I've gotten the wrong answer using this method. What gives?

 

[Mrspi]

In precalculus, we are learning to find the minimum or maximum of a quadratic equation.

A "trick" they gave us was x = -b/2a for ax^2+bx+c where a =/= 0.

-b/2a is supposed to be a shortcut for finding the maximum or minumum of a quadratic function but it is not working for me. Here is an example:

T=2b^2-12b+36

When I change it into standard for, I get 2(b-3)^2 + 18 which would suggest that the minimum is 18. However, when I apply the formula above, I get:

-(-12) / 2(2) = 12 / 4 = 3.

This is the second time I've gotten the wrong answer using this method. What gives?

When a quadratic function is in the form

y = ax[sup:1bumv3z1]2[/sup:1bumv3z1] + bx + c, then the maximum or minimum value of y occurs when x = -b/(2a)

The actual maximum or minimum value is the value of y....

You've got

T = 2b[sup:1bumv3z1]2[/sup:1bumv3z1] - 12b + 36

Or, to put it in the more usual "standard form": y = 2x[sup:1bumv3z1]2[/sup:1bumv3z1] - 12x + 36

So, the maximum or minimum value occurs when x = -(-12)/(2*2), or x = 12/4, or 3.

What is the value of y when x = 3?

Or, in terms of your original problem, what is the value of T when b = 3?

T = 2(3)[sup:1bumv3z1]2[/sup:1bumv3z1] - 12(3) + 36

Looks like you will get a value of 18 for T...which agrees with your analysis.

 

[tkhunny]

How strange of you to blame it on the tried and true formula? Why not, instead, read the definition again. Better yet, learn how to derive it and see how it works for yourself.

BOTH are correct.

18 is, indeed, the minimum value, but this has little to do with -b/(2a)

3 is, indeed, the value of the independent variable that produces 18 in the dependent variable, This is the intent of -b/(2a)

The location of the minimum point is (3,18).

If you spend your time looking for tricks, they WILL bite you eventually.

 

[nolsen01]

Yes I see, thank you. Since going back to school to study math I've been making these stupid little nonsense mistakes. It something that I need to work on.

How strange of you to blame it on the tried and true formula? Why not, instead, read the definition again. Better yet, learn how to derive it and see how it works for yourself.

BOTH are correct.

18 is, indeed, the minimum value, but this has little to do with -b/(2a)

3 is, indeed, the value of the independent variable that produces 18 in the dependent variable, This is the intent of -b/(2a)

The location of the minimum point is (3,18).

If you spend your time looking for tricks, they WILL bite you eventually.

Well, I'm not one for tricks either so I've been doing it the long way. However, since my professor gave us this formula I figured I should learn how to use it and obviously I was having problems.

Of course I do not blame my problems on the "tried and true" formula, or else I would not have come here to ask for help.

 

[tkhunny]

No need to make excuses or explain away errors. Learning is what is important. If you have a formula, you must learn exactly when it applies and exactly what it does. This gives you three things to memorize. If you create formulas through your own exploration, there is only one thing to memorize.