y=-x²+1

To find the x-intercepts of the equation y = -x^2 + 1, we set y to zero and solve for x:

0 = -x^2 + 1

Rearranging the equation, we have:

x^2 = 1

Taking the square root of both sides, we get:

x = ±√1

Therefore, the x-intercepts of the equation are x = -1 and x = 1.

To find the y-intercept, we set x to zero and solve for y:

y = -0^2 + 1

y = 1

Therefore, the y-intercept of the equation is y = 1.

To plot this on a graph, we can create a table of values:

x | y

-2 | -3 -1 | 0 0 | 1 1 | 0 2 | -3

Then, we can plot these points on a Cartesian plane and draw a curve that passes through them. The graph will be a downward-facing parabola with its vertex at (0, 1).