What is the y-intercept of $ y=(x+3)^2(x-1) $?

Question

BlackTom AI · Accepted Answer

We start by identifying what the y-intercept represents: the point where the graph crosses the y-axis, which occurs at x = 0.
Option a. (0,3): If we plug x = 0 into y = (x+3)^2(x-1), we get y = (0+3)^2(0-1) = 9(-1) = -9, not 3. Therefore this point is incorrect.
Option b. (0,9): Using the same substitution, y = -9, so the y-intercept is not 9. This option is incorrect.
Option c. (0,-9): Substituting x = 0 yields y = -9, which matches the computed value. This is the y-intercept of the function.
Option d. (0,-3): Again, substituting x = 0 gives -9, not -3. Hence this option is incorrect.

In summary, evaluating the function at x = 0 directly provides the y-coordinate of the y-intercept, which is -9, corresponding to the point (0,-9). The remaining choices fail because they do not match the actual output of the function at x = 0.

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