Question

How do you find the minimum and maximum value of `y=2(x-3)(x-5)`?

Answer 1

Maximum value is `(oo)` , minimum value is `-2`

Explanation:

`y=2(x-3)(x-5) = 2x^2 -16x +30 :. a = 2, b= -16 , c= 30; [y=ax^2+bx+c]`

Discriminant `D= b^2-4ac = 256-240=16`

Here roots are real `x=3 and x=5 and a>0`

When roots are real and `a>0` , Maximum value is `(oo)` and
minimum value is `-D/(4a) = -16/(4*2) = -2`. This is also confirmed from graph. graph{2x^2-16x+30 [-10, 10, -5, 5]} [Ans]