Question

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

Answer 1

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