How to Find 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. This article introduces the tools for finding 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

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).

Test Yourself

What is the y-intercept of y = 4x2 - 3x?

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

The y-intercept is (0,0).