How to find the y-intercept of a parabola?
Understand the Problem
The question is asking for the method to determine the y-intercept of a parabola. To find the y-intercept, you typically set the value of x to zero in the equation of the parabola and solve for y.
Answer
The y-intercept of the parabola is \( c \).
Answer for screen readers
The y-intercept of the parabola is ( c ).
Steps to Solve
- Identify the equation of the parabola
Make sure you have the equation of the parabola in standard form, which is usually $y = ax^2 + bx + c$.
- Set ( x = 0 )
To find the y-intercept, substitute ( x = 0 ) into the equation. This step simplifies the equation to find the value of ( y ).
- Solve for ( y )
After substituting ( x = 0 ), you will have:
$$ y = a(0)^2 + b(0) + c $$
This simplifies to ( y = c ).
- State the y-intercept
The y-intercept of the parabola is the value of ( y ) when ( x = 0 ), which is ( c ).
The y-intercept of the parabola is ( c ).
More Information
The y-intercept represents the point where the parabola crosses the y-axis. In terms of coordinates, this point can be represented as ( (0, c) ).
Tips
- Forgetting to substitute ( x = 0 ) correctly and using the wrong values in the equation.
- Misinterpreting the equation of the parabola; ensure it’s in the correct form to identify ( c ) accurately.
