如何将一个像元设置为ay值，并让一个公式确定二次方程式中的x值？

Question

I have a trend line equation of y=0.0031x^2 + 0.1336x + 0.0355. I have the y values in a column and I want to determine the x value for each via formula so I dont have to manually do the calculation 120 times.

Answer 1

You'd have to solve each one as a quadratic equation

So for a y-value y you'd have

a*x^2 + b*x + c = y

so

a*x^2 + b*x + (c-y) = 0

and you need the roots of

a*x^2 + b*x + c' = 0

where

c' = c-y

So if you put 0.0031 in A2, 0.1336 in B2 and 0.0355 in D2, The y-values starting in E2 say and then put the values of c' starting in C2 using

=$D$2-E2

you can get one set of x-values by

=(-$B$2+SQRT($B$2*$B$2-4*$A$2*C2))/(2*$A$2)

and the other set of x-values by

=(-$B$2-SQRT($B$2*$B$2-4*$A$2*C2))/(2*$A$2)

Have added two columns to check value of y calculated from x.

Answer 2

There is actually a Excel-Built-In mechanism to solve this kind of problem.

Lets say your y -Values are stored in the first column (A1, A2 and so on).

Then you will put the equation you are interested in, in C1, which will look like this, if we assume that the x -Value will be stored in D1:

=0.0031*POWER($D1,2)+0.1336*$D1+0.0355-A1

Drag down till suited.

Now put any number in D1, eg 5.

Drag D1 down till suited.

Go to the Data-Ribbon and go to the What-If-Analysis and choose the Goal-Seek.

It should look like this:

Please note that my Excel is German.

In the first field, you will choose the range in which the quadratic equation is located, in this case C1. In the second field, you will specify which value you would like to achieve. In this case 0. And in the third field, you will specify which range can be altered. In this case D1.

After pressing ok, excel will approximate the root of the function up to a accuracy of 10^-4.

You would have to do this by hand for all the value, or record a macro, see what excel does and write a short macro to do it for you.

It is also important to note, that this is only possible since Excel-2010. But since you have the excel 2016-tag you should be fine!

EDIT:

You can use this Macro, to do it for you, if you use the setup as described above:

Sub GS()

Dim rng As Range

For Each rng In Range("A1", "A4") '<~~ Change this to the range needed

    Cells(rng.Row, 3).GOALSEEK goal:=0, ChangingCell:=Cells(rng.Row, 4) 'Change 3 to the column your function is in. Change the 4 to the column you x-Value is in.

Next rng

End Sub