You have the following function:
f(x) = 4(x + 2)² - 1
In order to find the vertex of the previous function, expand the factor (x + 2)²:
f(x) = 4(x² + 4x + 4) - 1
f(x) = 4x² + 16x + 16 - 1
f(x) = 4x² + 16x + 15
the previous result has the general form:
f(x) = ax² + bx + c
by comparing the previous expression with the result for the given function you have:
a = 4
b = 16
c = 15
the vertex of the function f(x) is given by:
x = -b/2a
by replacing the values of parameters b and a you obtain:
x = -16/2(4)
x = -16/8
x = -2
Next, to find the vertex, it is necessary to calculate f(-2):
f(-2) = 4(-2 + 2)² + 1
f(-2) = 0 + 1
f(-2) = 1
Hence, the vertex is (-2,1)
