Find a polynomial function whose graph passes through (6,13),(10,-10) and (0,5)

See below

Step-by-step explanation:

Let the function be quadratic as the given points are not collinear, not a linear function

Standard form of quadratic equation:

Substituting the coordinates, we get:

From equation 3 we get c = 5, considering this in the other equations and simplifying:

Subtract 3 times the second equation from 2 times the first:

Finding the value of b:

The quadratic function is:

So the graph of any polynomial function:

will pass through the given 3 points