Question

Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum. (To clarify, 1/2 is a fraction *x^2)
1. (-1,0);minimum
2.(-1,0);maximum
3.(0,1);maximum
4.(0,-1);minimum

Answer 1

$y= -\frac{1}{2} x^{2}-1$ is a quadratic function, so its graph is a parabola.

Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.

That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.

for x=0, y=-1. So the vertex is (0, -1)

The coefficient of $x^{2}$ is negative. This means that the parabola opens downwards, so the vertex is a maximum.


Answer: (0, -1) , maximum (none of the choices)