STEP 1: Recall what is a factored form of a quadratic function with zeros

The factored form of a quadratic function is

f(x) = a( x- r_{1})(x - r_{2}) where r_{1},r_{2} are the two zeros.

STEP 2: Plug in the zeros of the quadratic function

r_{1} = 2 ; r_{2} = -2

f(x) = a( x-2)(x+2))

At y = -4 we have x = 0

So, plugging in x = 0 in the above equation

-4 = f(x) = a(0-2)(0+2)

-4 = a(-4)

a = 1

STEP 3: Write the equation of the quadratic function/parabola

y = 1(x-2)(x+2)

y = x^{2}-4

Skills to recall:

What is a quadratic function

http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/PandR/quadratic/quadratic.html

What is a parabola

https://www.qalaxia.com/viewDiscussion?messageId=5ceca64f0a8962539044ad8b

What are the x-and the y-intercepts of the parabola

https://www.mathwarehouse.com/geometry/parabola/parabola-intercepts.php

What is a factored form of a quadratic function