PLEASE HELP ASAP

Find the function with x-intercepts (-2, 0) and (4, 0), which also goes through the point (-1, 10).

Option D: is the function

Explanation:

Let the general form of quadratic equation be

The function passes through the intercepts and and also passes though the point

Substituting the points , and in the equation , we get,

 -----------(1)

----------(2)

   -----------(3)

Subtracting (1) and (2), we get,

 -----------(4)

Subtracting (2) and (3), we get,

 ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

Thus, the value of a is

Substituting in equation (4), we get,

Thus, the value of b is

Now, substituting the value of a and b in equation (1), we have,

Thus, the value of c is

Now, substituting the value of a,b and c in the general formula , we get,

Taking out the common term as -2 we get,

Factoring , we get,

Thus, the function is

there are infinitely many solutions.