### 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

### 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).

### 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).

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

*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).

### Picture of Example 3

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

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

What is the *y*-intercept of the following function?

y= 4x^{2}- 3x

### Answer to Example 4

*y *= 4*x*^{2} - 3*x*

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).