Question

What is the minimum value for the function
y= 2x^2 - 32x +256

Answer 1

you can use simple algebra (completing the square) or differential calculus to get the minimum. Which do you prefer?

Answer 2

simple algebra.

Answer 3

Start with the format of the equation you have: y = ax^2 + bx + c This equals y = a[x^2 + (b/a)x] + c Take half of b/a and square it, adding and subtracting it to the right side so you still have the same equation. y = a[x^2 + (b/a)x + (b^2)/(4a)] + c - (b^2)/(4a) Get the square expression of the expression in brackets: y = a[x + (b/2a)]^2 + c - (b^2)/(4a) Now, this is essentially the same (just rewritten) as your original equation. Works the same way. Graphs the same way. Same domain and range. It's the same. But now, we can see that the smallest value for [x + (b/2a)]^2 is 0 and that is when x = -b/2a, so the smallest the whole right side can be is c - (b^2)/(4a) and that is for y and that is when x = -b/2a.

Answer 4

i think i got it from here, thanks.