Checking form of equations

I have been using countNumberUsage in order to create a cellErrorMessage based on whether a student writes a quadratic in standard form, vertex form, or factored form. The error message looks for defined values that should be in each string (i.e. standard form looks for B and C). The errorMessage is successful as long as A,B,C, h,k, root1, and root 2 are all whole numbers.

For example, an equation like x^2-8 it would not recognize the factored form since it contains square roots. I even made a work around so that it would look for the square the radicand “k”. This would check for (x-sqrt(8))(x+sqrt(8)), but not the equivalent 2sqrt(2). Needless to say, validating based on form has proven to be a difficult undertaking. I was not sure if there was some other function that might be more useful for this.

Also, I am using a table in conjunction with an action button and random number generator. Is there a way to clear the table entries after each “submission” / graph regeneration?