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

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

No. The y-intercept is the value of y when x=0, hence it intersects the y-axis when x=0. In this case:

0^2-4(0)+y^2=-3

y^2=-3

y=√-3

Since there is no real square root of a negative value, the curve does not intersect the y-axis

A

Step-by-step explanation:

The answer is C) No, because the circle is entirely in the first quadrant

No it a first quadrant

No it does not intersect the y-axis

https://www.desmos.com/calculator

got to this site plug in that equation it will give you graph,you can see its not intersecting the y-axis

Step-by-step explanation:

B) No, because the center is a (2, 0) and the radius is 1

Yes, because the center is on the x-axis.

Step-by-step explanation:

First, write the equation in standard form by completing the square.

x2 - 4x + y2 = -3

x2 - 4x + 4 + y2 = -3 + 4

(x - 2)2 + y2 = 1

The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).

Yes, twice

Step-by-step 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

[tex]20 ! does the equation x2 - 4x + y2 = -3 intersect the x-axis?[/tex]

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

No, because the center is a (2, 0) and the radius is 1.

Step-by-step explanation: