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: Recall what is the y-intercept of the parabola

As evident from the graph the parabola touches the x-axis at 1 and -3.

Plug in the zeros of the quadratic function

r_{1}=-3, r_{2} = 1

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

At y = -3 we have x = 0

So, plugging in x = 0 in the above equation

-3 = f(x) = a(0-3)(0+1)

-3 = a(-3)

a = 1

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

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

y = x^{2}+2x -3

Further skills to recall"

Recall what is a quadratic function

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

Recall what is a parabola

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

Recall the x- and the y-intercepts of a parabola

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