The y-intercept in any equation is the point at which the line crosses the y-intercept. A quadratic equation is one where the dominate term is the x^2 term and typically results in a parabola that opens either upward or downward so it has only one y-intercept. Since the y-intercept occurs when the x-coordinate is zero, you can find it by setting the x variables in the equation to zero.
Insert zero for each x variable in the quadratic equation. For example, if your equation equals x^2 + 2x + 5, you would insert 0 for each x so the equation would be 0^2 + 2*0 + 5.
Simplify the equation to find the y-coordinate of the y-intercept. Here, 0^2 + 2*0 + 5 simplifies to 5, so the y-coordinate of the y-intercept equals 5.
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Write the y-intercept in coordinate form by plugging it into the following form: (0, y). Here, since the y-intercept is 5, you would plug in 5 for y to get a y-intercept coordinate of (0, 5).