# Highest standard in curve fit has no calculated concentration - WKB281661

## SYMPTOMS

- A quadratic curve was fitted to the observed values of standards. For most standards an "expected
*y*" was calculated from the observed*y*values using the equation that describes the standard curve, but for the highest concentration standard the calculated*x*cell is blank, as is the % deviation.

## ENVIRONMENT

- UNIFI

## CAUSE

Quadratic equations describe parabolas. So when you go beyond the highest point in the observed data the curve could continue upward, flatten, or start to drop downward. This means that for any given value of *y*, solving the equation for *x* has two possible answers, one to the left of the peak of the parabola and one to the right of the peak of the parabola. If an observed value for *y* lies within the range of observed *y*s for the standards, we assume the unknown lies on the left of the parabola and calculate the values of *x* based on the upward curve. But if the observed *y* is above the highest observed standard, you cannot assume which side of the parabola it lies on. This means you cannot extrapolate a quadratic curve beyond the range of the standards used to create it.

Using an online calculator tool (e.g., https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php), the quadratic equation shown in the above screenshot has the following possible solutions for the last value of *y* (i.e., 1.367), *x* = 164.184 or *x* = 187.961.

Both of these are outside the observed *x* values in the data set used to derive the standard curve. So when UNIFI tries to solve the quadratic line of best fit for the highest *y* value, that *y* has two possible x values, and because there is no mathematically valid way to determine which is right, UNIFI leaves "Calculated X" blank. Because it has no calculated *x* value to work with, it cannot determine the percentage deviation of the calculated *x* from the expected *x*, and % Deviation is also blank.

## FIX or WORKAROUND

None

## ADDITIONAL INFORMATION

id281661,