Question

20 points!!! Please Help

Does the equation x2 - 4x + y2 = -3 intersect the x-axis?

Answer 1

Yes, because the center is on the x-axis, the circle will intersect 2 times, at x=1 and at x=3

Answer 2

Yes, twice

Explanation:

The equation will intersect the x-axis when y = 0, so we have

x² - 4x = -3 now solve this quadratic for x...

x² - 4x + 3 = 0

factor...

(x - 3)(x - 1) = 0,

so at x = 1 and x = 3, the function crosses the x-axis

See the graph below