You have the followin function:
f(x) = -4x² + 16x + 47
take into account that the axis of symmetry of the previous function is given by the value of the x-coordinate of the vertex of the function.
Such vertex is given by teh following expression:
x = -b/2a
where a and b are the coefficients of the genereal form of a quadratic function, given by:
f(x) = ax² + bx + c
by comparin the previous expression witht he given f(x) you have that:
a = -4
b = 16
replace the previous values into the expression for x:
x = -16/(2(-4))
x = -16/(-8)
x = 2
for x = 2, there is the vertex of the function. A vertical line that crosses the x axis at x= 2 is the axis of symmetry of the given function.
The axis of symmetry is then:
x = 2
