Find the equation of the quadratic function with zeros - 1 and 1 and a vertex at (0,-4)

The equation is f (x) = 4x^2 - 4.

You can find this by using an equation with parenthesis that equal each of the zeros.

f (x) = (x - 1) (x + 1)

Now, this equation will not give us the vertex that we're looking for. So, we must add a constant being multiplied to the front of it.

f (x) = c (x - 1) (x + 1)

Now we can find the constant by putting our vertex into the equation and solving.

f (x) = c (x - 1) (x + 1)

-4 = c (0 - 1) (0 + 1)

-4 = c (-1) (1)

-4 = - 1c

c = 4

Now we put the c into the original equation and solve for standard form.

f (x) = 4 (x - 1) (x + 1)

f (x) = 4 (x^2 - 1)

f (x) = 4x^2 - 4