The y-intercept of a quadratic equation is the point where the graph of the equation intersects the y-axis. This occurs when the value of x is zero.
A quadratic equation is typically expressed in the standard form: y = ax² + bx + c, where:
- a is the coefficient of the quadratic term (x²),
- b is the coefficient of the linear term (x), and
- c is the constant term.
To find the y-intercept, we substitute 0 for x in the equation:
y = a(0)² + b(0) + c = c
This means that the y-intercept is simply the value of c in the equation. In graphical terms, the y-intercept gives us important information about the position of the parabola relative to the y-axis. Knowing the y-intercept can help in sketching the graph of the quadratic equation.