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

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= 12x^{2}+ 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 (Replacexwith 0.)

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

y= 0 + 0 + 49 (simplify)

y= 49 (simplify)

The *y*-intercept is (0, 49).

## Test Yourself

Find the y-intercept of

y = 4x^{2}- 3x

using the following steps:

y= 4(0)2 - 3(0) (Replacexwith 0.)

y= 4* 0 - 0 (simplify)

y= 0 - 0 (simplify)

y= 0 (simplify)

The *y*-intercept is (0,0).