The graph the function represented by the equation g(x) = -(x + 4)² + 1 is attached
How to graph the function represented by the equation
From the question, we have the following parameters that can be used in our computation:
g(x) = -(x + 4)² + 1
The axis of symmetry is calculated as
x + 4 = 0
So, we have
x + 4 = 0
x = -4
Next, we have the y-coordinate of the vertex to be
g(-4) = -(-4 + 4)² + 1
g(-4) = 1
So, the vertex is (-4, 1)
For the y-intercept, we have
g(0) = -(0 + 4)² + 1
g(0) = -15
Lastly, the increasing and decreasing intervals are (-∝, -4) and (-4, ∝), respectively
The graph is attached