How many real zeroes does y = (x + 8)^3 + 9 have?

Question

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- 0

Answer 1

The equation y = (x + 8)^3 + 9 is a cubic equation.

To determine the number of real zeroes, we can analyze the end behavior of the equation. As x approaches positive infinity, (x + 8)^3 becomes increasingly positive. Adding 9 to the positive value results in a positive y value. Similarly, as x approaches negative infinity, (x + 8)^3 becomes increasingly negative. Adding 9 to the negative value also results in a negative y value.

Since the end behavior of the equation results in a positive y value as x approaches negative or positive infinity, there must be no real zeroes.

Therefore, the correct answer is 0.