Question

which is the axis of symmetry of ( f(x) = 3(x - 85)^2 + 200 )?

a ( x = 85 )

b none of these

c ( x = 3 )

d ( y = 85 )

e ( x = 200 )

f ( x = -85 )

g ( y = 200 )

h ( x = 0 )

i ( y = 0 )

Explanation:

Step1: Recall Vertex Form

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where the axis of symmetry is \( x = h \).

Step2: Identify \( h \) in Given Function

For \( f(x) = 3(x - 85)^2 + 200 \), compare with \( a(x - h)^2 + k \). Here, \( h = 85 \).

Step3: Determine Axis of Symmetry

Using the vertex form rule, the axis of symmetry is \( x = h \), so \( x = 85 \).

Answer:

A. \( x = 85 \)