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Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :

(i) the minimum value of f(x).
(ii) the value of x for which f (x) is a minimum

User Annalisa
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1 Answer

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Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1 (-1)^2 = 1

Add 1 (But remember the 3 out front so we are really adding 3 so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k where (h,k) is the vertex and a is a constant

The vertex is (1,-21)

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

User Savion
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