Finding the y-intercept of a Parabola

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Finding the y-intercept of a Parabola

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.

How to Find the y-intercept

This article introduces the tools for finding the y-intercept.

  • The graph of a quadratic function
  • The equation of a quadratic function
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Example 1: Use a Parabola to Find the y-intercept

Place your finger on the green parabola. Trace the parabola until your finger touches the y-intercept.

Notice that your finger touches the y-axis at (0,3).

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Example 2: Use the Parabola to find the y-intercept.

Place your finger on the green parabola. Trace the parabola until your finger touches the y-intercept.

Notice that your finger touches the y-axis at (0,3).

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Example 3: Use the Equation to Find the y-intercept

What is the y-intercept of this parabola? 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. Notice that the x-value is always 0. So, plug in 0 for x and solve for y.

  1. y = 12(0)2 + 48(0) + 49   (Replace x with 0.)
  2. y = 12 * 0 + 0 + 49    (Simplify.)
  3. y = 0 + 0 + 49           (Simplify.)
  4. y = 49                       (Simplify.)

The y-intercept is (0, 49).

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Picture of Example 3

Notice that the y-intercept is (0, 49).

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Example 4: Use the Equation to Find the y- intercept

What is the y-intercept of the following function?

y = 4x2 - 3x


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Answer to Example 4

y = 4x2 - 3x

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

The y-intercept is (0,0).

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Your Citation
Ledwith, Jennifer. "Finding the y-intercept of a Parabola." ThoughtCo, Oct. 3, 2016, thoughtco.com/finding-the-y-intercept-of-parabola-2312308. Ledwith, Jennifer. (2016, October 3). Finding the y-intercept of a Parabola. Retrieved from https://www.thoughtco.com/finding-the-y-intercept-of-parabola-2312308 Ledwith, Jennifer. "Finding the y-intercept of a Parabola." ThoughtCo. https://www.thoughtco.com/finding-the-y-intercept-of-parabola-2312308 (accessed May 24, 2018).