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anonymous
 5 years ago
A function is defined as f(x)=ax^2+bx+d, where a, b, and d are integers.
The minimum value of f(x) is 4
Determine the xcoordinate of the minimum value of f(x) and hence find the value of d.
anonymous
 5 years ago
A function is defined as f(x)=ax^2+bx+d, where a, b, and d are integers. The minimum value of f(x) is 4 Determine the xcoordinate of the minimum value of f(x) and hence find the value of d.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay, well you know that at some x the minimum is 4, so you can find that point by taking the derivative of f(x) and setting it to 0 which is: \[2ax +b = 0\] so \[x = b/2a\] then you can place that in the first equation: \[ax^2 + bx + d = a(b/2a)^2 + b(b/2a) + d = b^2/2a b^2/2a + d = 4\] thus \[d = 4\] then you can find x by setting f(x) = 4 and then solving for x, which gives \[4 = ax^2 +bx 4 > 0 = ax^2+bx = x(ax + b)\] so you can say that \[x = 0, b/a\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry haha, math error :O. just noticed. should be \[b^2/4a^2  b^2/2a + d = 4\] which would change everything. its kinda late here......sorry.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so then \[x = b/2a\] and \[d = (16a^2 +b^2(2a1))/4a^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not \[4a^2\] i meant \[4/a\]....I am going to bed.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So to actually put it together nicely. \[x=b/2a\] and \[d = 4  b^2/4a + b^2/2a = 4 + b^2/4a\].
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