To find the y-intercept of a quadratic function in factored form, substitute x = 0 into the equation and solve for y. The resulting y-value is the y-intercept.
Steps to Find the Y-Intercept
Here's a breakdown of how to find the y-intercept when your quadratic function is in factored form, such as y = a(x - r)(x - s), where 'a' is a constant, and 'r' and 's' are the roots:
-
Substitute x = 0: Replace every instance of 'x' in the factored form equation with the number 0.
-
Simplify: Perform the arithmetic operations within the parentheses and then multiply the resulting numbers together, including the constant 'a'.
-
The result is the y-intercept: The value you get for 'y' after simplifying is the y-coordinate of the y-intercept. The y-intercept is the point (0, y).
Example
Let's say you have the quadratic function: y = 3(x + 2)(x - 5)
-
Substitute x = 0:
y = 3(0 + 2)(0 - 5) -
Simplify:
y = 3(2)(-5)
y = 3 * -10
y = -30 -
The y-intercept is -30: The y-intercept is the point (0, -30).
Therefore, the y-intercept of the quadratic function y = 3(x + 2)(x - 5) is -30. This means the parabola crosses the y-axis at the point (0, -30).
