How to find the y-intercept of a polynomial?
Understand the Problem
The question is asking how to determine the y-intercept of a polynomial function. The y-intercept is found by evaluating the polynomial at x = 0, which gives us the value of y when the graph intersects the y-axis.
Answer
The y-intercept is $c$.
Answer for screen readers
The y-intercept of the polynomial function is the constant term, denoted as $c$.
Steps to Solve
- Identify the polynomial function
You need to know the specific polynomial function you're working with. For example, if the polynomial is $f(x) = ax^2 + bx + c$, identify the values of $a$, $b$, and $c$.
- Substitute x with 0
To find the y-intercept, substitute $x = 0$ into the polynomial function.
For the example function $f(x) = ax^2 + bx + c$, we substitute:
$$ f(0) = a(0)^2 + b(0) + c $$
- Simplify the expression
Calculating the expression gives:
$$ f(0) = 0 + 0 + c = c $$
- Determine the y-intercept
The y-intercept is represented by the value you found. In our example, the y-intercept is $c$, which is the constant term of the polynomial function.
The y-intercept of the polynomial function is the constant term, denoted as $c$.
More Information
The y-intercept is the point at which the graph of a function crosses the y-axis. This value is essential to understand the position and shape of the graph, particularly in polynomial functions.
Tips
- Forgetting to substitute $x = 0$—Always remember to replace $x$ with $0$ to find the y-intercept.
- Misidentifying the constant term—Double-check which term is the constant in your polynomial function.
