Determine the quadratic function f whose graph is given.
the vertex is (-2,-7)
y intercept -3

f(x)=

Use the vertex form y = a(x - h)^2 + k.

Use the points from the vertex (-2, 7) and plug them into the 'h' and 'k' variables (h, k) with -2 being 'h' and 7 being 'k'

y = (x + 2)^2 - 7
y + 7 = (x + 2)^2
y + 7 = (x + 2)(x + 2)
y + 7 = x^2 + 4x + 4
y = x^2 + 4x - 3

The quadratic function is
y = x^2 + 4x - 3

Hope this helps!