Question

module 4 / lesson 60

1. identify the vertex of the function $f(x) = -2(x + 3)^2 - 12$.

\bigcirc \\ (3, -12)
\bigcirc \\ (-2, -12)
\bigcirc \\ (-2, -3)
\bigcirc \\ (-3, -12)

Explanation:

Step1: Recall the vertex form of a parabola

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

Step2: Rewrite the given function in vertex form

The given function is \( f(x) = -2(x + 3)^2 - 12 \). We can rewrite \( (x + 3) \) as \( (x - (-3)) \), so the function becomes \( f(x) = -2(x - (-3))^2 + (-12) \).

Step3: Identify \( h \) and \( k \)

Comparing with the vertex form \( f(x) = a(x - h)^2 + k \), we have \( h = -3 \) and \( k = -12 \). So the vertex is \((h, k) = (-3, -12)\).

Answer:

\( (-3, -12) \)