How to Find the Y-Intercept of a Quadratic Function in Vertex Form?

To find the y-intercept of a quadratic function in vertex form, substitute x = 0 into the equation and solve for y.

Here's a breakdown of the process:

1. Understand Vertex Form: The vertex form of a quadratic equation is given by:

   y = a(x - h)^2 + k

   where:

   • (h, k) represents the vertex of the parabola.
   • a determines the direction and "width" of the parabola.

2. Substitute x = 0: To find the y-intercept, we need to find the value of y when x is zero. So, replace x with 0 in the equation:

   y = a(0 - h)^2 + k

3. Simplify and Solve for y: Simplify the equation and solve for y. This will give you the y-coordinate of the y-intercept. The y-intercept is the point (0, y).

Example:

Let's say you have the quadratic function in vertex form:

y = 2(x - 1)^2 + 3

1. Substitute x = 0:

   y = 2(0 - 1)^2 + 3

2. Simplify:

   y = 2(-1)^2 + 3
y = 2(1) + 3
y = 2 + 3
y = 5

Therefore, the y-intercept is (0, 5).

In summary, the key is to replace x with zero in the vertex form equation and then isolate and solve for y. The resulting y value gives you the y-coordinate of the y-intercept.