.
If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. Firmly memorize this:
A quadratic function y = has a minimum/maximum at x = . (1)
To find this maximum/minimum value, substitute x = into the quadratic function.
Then min/max, after calculations, is . (2)
Next, if a > 0 then the parabola is open up and the min/max is the minimum.
If a < 0 then the parabola is open down and the min/max is the maximum.
2. In your case, the minimum is at s = = 2.
To calculate , substitute s = 2 into the quadratic function. It will produce the same value as (2), but the calculations are easier.
= = 8 - 16 + 19 = 11.
See the lesson Who is who in quadratic equations in this site.
Next, memorize this:
It doesn't matter which letter of the English alphabet is used in the parabola equation as a variable.
To find a min/max and a vertex coordinates, always use the formula (1). It works ALWAYS.
After finding x, calculate the value of a min/max by substituting the found value of "x" into the parabola equation.
And the last notice.
There is no need to use so many symbols "$" as you do.
We understand clearly your formulas without it.