Answer:
f(x) = -(x + 2)² − 2
f(x) = -x² − 4x − 6
Step-by-step explanation:
Equation of a parabola is:
y = a (x − h)² + k
where (h, k) is the vertex.
Assuming that (-2, -2) is the vertex:
y = a (x − (-2))² + (-2)
y = a (x + 2)² − 2
Since (-5, -11) is a point on the parabola:
-11 = a (-5 + 2)² − 2
-9 = 9a
a = -1
Therefore, the equation of the parabola is:
y = -(x + 2)² − 2
Which simplifies to:
y = -x² − 4x − 6
