Question

question 19 (mandatory) (1 point) saved
which coordinate is the vertex of the function ( f(x) = -4(x - 3)^2 - 9 )

a) ( (3, 9) )

b) ( (9, -3) )

c) ( (3, -9) )

d) ( (12, -9) )

Explanation:

Step1: Recall vertex form of 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: Identify \( h \) and \( k \) from given function

For the function \( f(x) = -4(x - 3)^2 - 9 \), compare it with the vertex form. Here, \( h = 3 \) (since it's \( x - 3 \)) and \( k = -9 \) (since it's \( + (-9) \)). So the vertex is \((h, k)=(3, -9)\).

Answer:

c) (3, -9)