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What is the minimum possible value of x^2 – 6x + 14?

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Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
For a quadratic function of the form ax^2 + bx + c where a>0, the minimum value of the function is given by 4ac–b^2/4a

Putting values:
4*1*14 - (6)^2 /4*1 = 20/4 = > 5

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What is the minimum possible value of x^2 – 6x + 14? [#permalink]
Bunuel wrote:
What is the minimum possible value of $$x^2 – 6x + 14$$?

A. 0
B. 1
C. 5
D. 6
E. 14

No formula approach.

$$x^2 – 6x + 14$$ = $$x^2 – 6x + 8 + 6$$ = $$x^2 – 2x - 4x + 8 + 6$$ = (x-2) (x-4) + 6

Remember here, $$x\geq{2}$$. Now at x = 2,4 the the value will be 6 , but at x=3, the minimum value will be 5.

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Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
Think of it as 10+x^2.
For us to get the minimum value, we can only assign x to 0 (x=0).
Since there is no point in assigning a negative number because of the square.
Now let's work on the question.

x^2–6x+14
x^2-6x+9+5
(x^2-2.x.3+3^2)+5
(x-3)^2+5

So, the minimum value here is 5.

ANS is C.
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Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
The minimum value of a quadratic equation occurs at $$\frac{-b}{2a}$$

The minimum value will occur at $$\frac{-(-6)}{2 \times 1} = 3$$

Putting the value $$x = 3$$ in the equation $$x^2 – 6x + 14$$

$$3^2 - 6 \times 3 + 14 = 9 + 14 - 18 = 23 - 18 = 5$$

OA, C
Bunuel wrote:
What is the minimum possible value of $$x^2 – 6x + 14$$?

A. 0
B. 1
C. 5
D. 6
E. 14
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Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
1
Kudos
b^2-4ac>= 0 ( because factor of x can be found by x = -b+(or-)sqrt ( b^2-4ac)/2a
i can only change value of c to find the minimum value of expression ( x^2–6x+14 )
36-4c>0 --> c=<9 ==> c= 9 for expression to have 0
current value of c is 14
so minimum value of given expression is 14-9 = 5 ( it would be (x-some factor)^2+ 5= 0
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Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
x^2–6x+14
= x^2-6x+9+5
= (x-3)^2+5
Minimum value of square term is 0
Therefore minimum value of the expression is 5
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Re: What is the minimum possible value of x^2 6x + 14? [#permalink]
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Re: What is the minimum possible value of x^2 6x + 14? [#permalink]
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