Answer:
- vertex: (-2, -1)
- axis of symmetry: x = -2
- graph: see below
Step-by-step explanation:
The equation is in vertex form ...
y = a(x -h)² +k . . . . . . . . vertex (h, k) and vertical scale factor "a"
y = (x +2)² -1
so, you can read the vertex coordinates directly from the equation:
(h, k) = (-2, -1)
__
The line of symmetry is the vertical line through the vertex, so has equation ...
x = h
x = -2 . . . . for this parabola
__
The vertex is always a point on the graph.
At x-values ±1 either side of the vertex, the vertical distance from the vertex is "a". Here, that is 1 unit, so the points (-3, 0) and (-1, 0) are on the graph.
At x-values ±2 either side of the vertex, the vertical distance from the vertex is a·2². Here that is 4 units, so the points (-4, 3) and (0, 3) are on the graph.
This is basically what the vertex form of the equation is telling you.
