How to find the y-intercept of a polynomial?
Understand the Problem
The question is asking for a method to determine the y-intercept of a polynomial function. The y-intercept can be found by evaluating the polynomial at x=0.
Answer
The y-intercept is \( k \).
Answer for screen readers
The y-intercept of the polynomial function is the constant term ( k ).
Steps to Solve
- Identify the Polynomial Function
Determine the polynomial function you are dealing with. Let's say it is represented as $P(x) = ax^n + bx^{n-1} + ... + k$.
- Evaluate the Polynomial at x=0
To find the y-intercept, substitute $x = 0$ in the polynomial function: $$ P(0) = a(0)^n + b(0)^{n-1} + ... + k $$
- Simplify the Expression
When simplifying the expression, all terms with $x$ will equal zero, leaving: $$ P(0) = k $$
- Conclusion
The y-intercept of the polynomial function is the constant term $k$.
The y-intercept of the polynomial function is the constant term ( k ).
More Information
The y-intercept is a crucial point on the graph of a polynomial function, representing where the graph crosses the y-axis. It is directly related to the constant term of the polynomial.
Tips
One common mistake is to forget that when evaluating at ( x=0 ), all terms containing ( x ) will vanish. Ensure to only focus on the constant term.
