What is the y-intercept of [math: y=(x+3)2(x−1)] y=(x+3)^2(x-1) ?

Question

BlackTom AI · Accepted Answer

To find the y-intercept of the graph given by y = (x+3)^2(x-1), we evaluate the function at x = 0 since the y-intercept is where the graph crosses the y-axis.

Compute y when x = 0: y = (0+3)^2(0-1) = 3^2 * (-1) = 9 * (-1) = -9.
Thus the y-coordinate of the intercept is -9, and the corresponding point is (0, -9).

Now review the answer options:
- Option a: (0, -3) would require y = -3 at x = 0, which would mean (0+3)^2(-1) = -3, contradicting the actual calculation since (0+3)^2 = 9, not 3.
- Option b: (0, 9) would require y = 9, but we computed y = -9, so this is incorrect.
- Option c: (0, -9) matches our computed value exactly.
- Option d: (0, 3) would require y = 3, which does not align with the evaluation at x = 0.

In summary, evaluating the function at x = 0 yields -9, so the y-intercept is (0, -9).

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