Question

which equation represents the equation of the axis of symmetry for $f(x) = -3(x + 4)^2 + 2$?
\bigcirc a) $x = 4$
\bigcirc b) $x = -4$
\bigcirc c) $x = 12$
\bigcirc d) $y = 2$

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Identify h in given function

For the function \( f(x)=-3(x + 4)^2 + 2 \), we can rewrite \( (x + 4) \) as \( (x - (-4)) \). So, comparing with \( a(x - h)^2 + k \), we have \( h=-4 \).

Step3: Determine axis of symmetry

Using the formula for the axis of symmetry from the vertex form, since \( h = -4 \), the axis of symmetry is \( x=-4 \).

Answer:

b) \( x = -4 \)