Final answer:
The vertex of the quadratic function is (-1, -8) and the axis of symmetry is x = -1.
Step-by-step explanation:
The given quadratic function is f(x) = (x+1)² - 8.
To find the vertex, we need to identify the values of x and y that make the function minimum or maximum. This occurs at the vertex.
The x-coordinate of the vertex can be found by using the formula x = -b/2a
where a and b are the coefficients of x² and x, respectively.
In this case, a = 1 and b = 2,
so x = -2/2
x= -1.
To find the y-coordinate of the vertex, substitute the x-coordinate into the function.
f(-1) = (-1+1)² - 8
= 0 - 8
= -8.
Therefore, the vertex is (-1, -8). The axis of symmetry is a vertical line that passes through the vertex. In this case, the axis of symmetry is the line x = -1.