Question

Which of the following describes the graph of y=x^2−144?

The graph has zeroes at x = -12 and x = -12 and it opens downward.

The graph has zeroes at x = 12 and x = -12 and it opens downward.

The graph has zeroes at x = 12 and x = 12 and it opens upward.

The graph has zeroes at x = 12 and x = -12 and it opens upward.

Answer 1

y=x^2-144 has zeros when

x^2-144=0

x^2=144

x=√144

x=±12

dy/dx=2x, and d2y/dx2=2 since acceleration is a constant positive when dy/dx=0, y(x) is at an absolute minimum. So the parabola opens upwards.

So the graph has zeros at -12 and +12 and opens upwards.