How to Find the Y-Intercept of a Parabola

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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:

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

The y-intercept is (0,0).