SOLUTION: If s is a real number, then what is the smallest possible value of 2s^2

SOLUTION: If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19?

Question 1026782: If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
is a quadratic polynomial.
Quadratic functions such as with {{a<>0}}} ,
have a maximum (if ),
or a minimum (if ).
So, since the coefficient of is ,
has a minimum value}}} .

How could you find that minimum value?
You could remember and apply a recipe handed down by your algebra 2 teacher.
Alternatively, you could use your knowledge of algebra, and your ability to think.

APPLYING MEMORIZED FORMULAS/RECIPES:
A quadratic function {{f(x)=ax^2+bx+c}}} with has a minimum for .
In the case of ,
the variable is rather than , and ,
so the minimum happens for ,
and for , .

IF YOU DID NOT MEMORIZE THAT FORMULA,
you have to reason your way to the answer.
may remind you of ,
and .
So, you can complete the square:
.
You know that the square of any real number is non-negative,
so , and ,
which means the the smallest possible value of is .
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