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*= 12*x*^{2}+ 48*x*+ 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*.

*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

What is the *y*-intercept of *y *= 4*x*^{2} - 3*x?*

*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).