Describe how the graph of y = -x² + 1 differs from y = x². Then find the axis of symmetry and the vertex.
I have no clue what this even means.
The graph of y=x^2 opens upwards, thus has a minimum value while the graph of y=-x^2 opens downwards and has a maximum value.
The axis of symmetry is the same for both of them. The axis of symmetry is where the mirror line for the function would sit. This is at x=0
The vertex is the max or min value. For y=x^2 if you sub in values for x of 0,1, -1, 2 and -2 you see that the minimum value occurs when x=0, so (0,0)
While... if you do the same thing for y=-x^2 + 1 you see the entire function opens downward and has a maximum value at (0,1)