Table to Equation – Method One (use the zeros (x-intercepts) and any other point)

To write an equation, you will actually use the coordinates of the points displayed in the table. We will use the same table for this example.

Using the coordinates of the x-intercepts, you can write an equation in factored form with the value of a, the coefficient of x²to be found:

Since the zeros (x-intercepts) occur when x = -1 and x = 3, we know the equation in factored form must be:

y = a(x +1)(x - 3)

Now, substitute the coordinates from one of the other points on the table, such as (-2, 10):

Note: x-values are indicated in red and y-values are indicated in green.

10 = a(-2+1)(-2-3)

And solve for 'a'

10 = a(-1)(-5)
10 = 5a
2 = a

Now, substitute the value for a back into your equation with your variables: