SOLUTION: Consider the quadratic function y＝kx(x-2)+3. If its optimum value is 4, find the value of k.

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Question 1005898: Consider the quadratic function y＝kx(x-2)+3. If its optimum value is 4, find the value of k.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=kx%5E2-2kx%2B3

k%3C0 and y=4 where x is the middle value between the zeros.

Finding zeros using formula for general solution of quadratic equation:
x=%282k%2B-+sqrt%284k%5E2-4k%2A3%29%29%2F%282k%29
D for discriminant,
x=%282k%2B-+sqrt%28D%29%29%2F%282k%29


Middle x between the zeros is %282k%2B2k%29%2F%282%2A2k%29
4k%2F4k
highlight%281%29
-
This means x=1 and y=4 is the maximum or "optimum" or VERTEX point for the function.

4=k%2A1%281-2%29%2B3 using the given original equation or function
4=k%28-1%29%2B3
4=-k%2B3
-4=k-3
k=-4%2B3
highlight%28k=-1%29