Consider the function 𝑃 ( 𝑥 )

To find the $y$-intercept of the function $P(x) = x^3 + 7x^2 + 10x$, we evaluate the function at $x = 0$.

1. Substitute $x = 0$ into $P(x)$: $P(0) = (0)^3 + 7(0)^2 + 10(0) = 0$

Thus, the $y$-intercept is the point $(0, 0)$.

Would you like a more detailed breakdown of this process or have any other questions?

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Here are five related questions to explore:

1. What are the $x$-intercepts of the function $P(x) = x^3 + 7x^2 + 10x$?
2. How would you find the critical points of $P(x)$?
3. What does the behavior of $P(x)$ look like as $x \to \infty$ and $x \to -\infty$?
4. Can we factorize $P(x) = x^3 + 7x^2 + 10x$ to find its roots?
5. How do we determine the turning points of a cubic function like $P(x)$?

Tip: The $y$-intercept of any function $f(x)$ is always found by evaluating $f(0)$.