Question

question 1 (mandatory) (1 point) saved
which equation represents the equation of the axis of symmetry for ( f(x) = -3(x + 4)^2 + 2 )?

a) ( x = 4 )

b) ( x = -4 )

c) ( x = 12 )

d) ( y = 2 )

Explanation:

Step1: Recall Vertex Form

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

Step2: Identify \( h \) in Given Function

For \( f(x) = -3(x + 4)^2 + 2 \), rewrite \( (x + 4) \) as \( (x - (-4)) \). So, \( h = -4 \).

Step3: Determine Axis of Symmetry

Using the formula for the axis of symmetry (\( x = h \)), substitute \( h = -4 \). Thus, the axis of symmetry is \( x = -4 \).

Answer:

b) \( x = -4 \)