How to Find the Y-Intercept of a Parabola

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Updated on December 09, 2019

A parabola is a visual representation of a quadratic function. Each parabola contains a y-intercept, the point at which the function crosses the y-axis. Learn the tools you need to find the y-intercept using the graph of a quadratic function and the equation of a quadratic function.

Use the Equation to Find the Y-Intercept

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Finding the y-intercept of a parabola can be tricky. Although the y-intercept is hidden, it does exist. Use the equation of the function to find the y-intercept.

y = 12x² + 48x + 49

The y-intercept has two parts: the x-value and the y-value. Note that the x-value is always zero. So, plug in zero for x and solve for y:

y = 12(0)² + 48(0) + 49 (Replace x with 0.)

y = 12 * 0 + 0 + 49 (simplify)

y = 0 + 0 + 49 (simplify)

y = 49 (simplify)

The y-intercept is (0, 49).

Test Yourself

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Find the y-intercept of

y = 4x² - 3x

using the following steps:

y = 4(0)2 - 3(0) (Replace x with 0.)

y = 4* 0 - 0 (simplify)

y = 0 - 0 (simplify)

y = 0 (simplify)

The y-intercept is (0,0).

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Ledwith, Jennifer. "How to Find the Y-Intercept of a Parabola." ThoughtCo, Jun. 25, 2024, thoughtco.com/finding-the-y-intercept-of-parabola-2312308. Ledwith, Jennifer. (2024, June 25). How to Find the Y-Intercept of a Parabola. Retrieved from https://www.thoughtco.com/finding-the-y-intercept-of-parabola-2312308 Ledwith, Jennifer. "How to Find the Y-Intercept of a Parabola." ThoughtCo. https://www.thoughtco.com/finding-the-y-intercept-of-parabola-2312308 (accessed June 24, 2025).