Find the y-coordinate of the y-intercept of the polynomial function defined below: f(x) = (x - 3)²
Understand the Problem
The question is asking to determine the y-coordinate of the y-intercept for the given polynomial function. To solve this, we substitute x = 0 into the function and simplify to find the corresponding y value.
Answer
The y-coordinate of the y-intercept is \( 9 \).
Answer for screen readers
The y-coordinate of the y-intercept is ( 9 ).
Steps to Solve
-
Identify the function The polynomial function given is ( f(x) = (x - 3)^2 ).
-
Substitute x = 0 To find the y-intercept, we substitute ( x = 0 ) into the function: $$ f(0) = (0 - 3)^2 $$
-
Calculate the value Now simplify the equation: $$ f(0) = (-3)^2 = 9 $$
-
Conclusion The y-coordinate of the y-intercept is ( 9 ).
The y-coordinate of the y-intercept is ( 9 ).
More Information
The y-intercept of a function is the point where it crosses the y-axis, which occurs when ( x = 0 ). In this case, substituting ( 0 ) into the polynomial reveals that the point is ( (0, 9) ).
Tips
- Forgetting to substitute ( x = 0 ) correctly.
- Making calculation errors while squaring a negative number.
AI-generated content may contain errors. Please verify critical information
