By Elliot Walsh
Updated Aug 30, 2022

Quadratic equations describe parabolic curves that open upward or downward. When graphed, they form a U‑shaped curve. Two key points on this curve are the x‑intercepts (where the parabola meets the x‑axis) and the y‑intercept (where it meets the y‑axis). This article explains how to locate the y‑intercept in each of the three common forms of a quadratic equation.

What Is the Y‑Intercept of a Quadratic Function?

The y‑intercept is the single point where the parabola crosses the y‑axis. Algebraically, it is the value of y when x = 0. In coordinate form it is written as (0, y).

Quadratic Equation Forms

Quadratic equations can be expressed in three standard formats:

• Standard form: y = ax² + bx + c
• Vertex form: y = a(x − h)² + k
• Factored form: y = a(x − r₁)(x − r₂)

Although the appearance differs, the method for finding the y‑intercept remains the same: evaluate the equation at x = 0.

Finding the Y‑Intercept in Standard Form

In standard form the constant term c is the y‑intercept. To verify, substitute 0 for x:

y = 5x² + 11x + 72

When x = 0:

y = 5(0)² + 11(0) + 72 = 72

Thus the y‑intercept is (0, 72).

Finding the Y‑Intercept in Vertex Form

In vertex form the constant term k is the y‑intercept. Substituting 0 for x gives:

y = 134(x + 56)² − 47

When x = 0:

y = 134(56)² − 47 = 134(3,136) − 47
   = 420,224 − 47 = 420,177

So the y‑intercept is (0, 420,177).

Finding the Y‑Intercept in Factored Form

In factored form substitute 0 for x directly:

y = 7(x − 8)(x + 2)

When x = 0:

y = 7(0 − 8)(0 + 2) = 7(−8)(2) = −112

Hence the y‑intercept is (0, −112).

Quick Tip

For standard and vertex forms, the y‑intercept is immediately visible as the constant term (c or k). Simply locate that number to find the y‑intercept without any calculation.

When in doubt, the universal method of substituting x = 0 works for all forms and confirms the result.