I am doing Quadratic Equations! Are Extremes the highest possible point? value?
2006-10-29 04:32:58 · 5 answers · asked by Jazz 2 in Science & Mathematics ➔ Mathematics
You may be thinking, why don't I just look it up in my textbook? My textbook is very confusing and doesn't explain what an extreme is.
2006-10-29 04:34:00 · update #1
x=-b +/- Square root (b squared -4ac) all over 2a
extremes are highest value, I think...
2006-10-29 04:43:43 · answer #1 · answered by rocker 3 · 0⤊ 0⤋
Yes, the extreme is the highest possible value. The only quadratics which will have extremes are the ones with a negative coefficient for the x^2 term; a positive x^2 coefficient means that the quadratic will have a minimum rather then a maximum.
2006-10-29 12:41:53 · answer #2 · answered by bruinfan 7 · 0⤊ 0⤋
Make a complete square out of the quadratic in question. Such as
ax^2+bx+c=a(x+b/2a)^2+(c-b^2/4a). Now the term (x+b/2a)^2 is always positive. The minimum value of it can only be 0. So if 'a' is positive, the minimum value of the quadratic ax^2+bx+c is only c-b^2/4a. There is no maximum value in this case, the value of the expression increases indefinitely as we increase x in case 'a' is positive and quickly nullifies c-b^2/4a however big negative it might have been imagined. This happens at x = - b/2a. In the same manner, if 'a' is negative, the expression runs to minus infinity as x increases; so the maximum value of the expression ax^2+bx+c is given by c-b^2/4a , for the maximum value of a(x+b/2a)^2 is 0 for any negative 'a'. Clearly this again happens at x = - b/2a. It is interesting to note that if the two values of the roots of ax^2+bx+c are equal then both of them are given by - b/2a. So the expression is maximum or minimum where the two roots 'would have been' equal !
2006-10-29 13:09:57 · answer #3 · answered by Anonymous · 0⤊ 0⤋
That's probably the best way for you to think of them. (And, BTW, they're 'extrema'. It's a Latin thang âº)
But, before you can talk about 'extrema', you have to have an 'interval' . That's the range of values that the independent variable (usually the x-axis variable) can assume. If you just say the extrema of x² + 2x + 1 then it's at ± â since the value of the function increases without bound as x increases without bound in either the positive or negative direction.
Doug
2006-10-29 12:48:42 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
Extrema can be a minimum value or a maximum value.
Also, they can be expressed as the minimum or maximum for the whole function, or only a certain interval (like from -1 to 2, or something like that).
2006-10-29 12:46:35 · answer #5 · answered by topher8128 2 · 0⤊ 0⤋