# How to Find the Y-Intercept of a Function

## Finding the Y-Intercept of a Function

The y-intercept of a function is found where the graph of a function crosses the y-axis on a pair of Cartesian coordinate axes.

## How to Find the Y-intercept of a Function

The y-intercept of a function **f(x)** is found by evaluating the function at **x = 0**.

This uses functional notation (see **Note**) to express the following idea.

The y-intercept is the value of the function at the y-axis. Along the y-axis, the value of **x** is 0. The input **x** of the function equals **0**.

The image below shows what we mean:

## A Real Example of How to Find the Y-intercept of a Function

Finding the y-intercept of a function is easy.

### Question

What is the y-intercept of the function **f(x) = 2x − 3**?

### Step-by-Step:

# 1

# 2

Substitute **x = 0** into the function.

f(0) = 2 × 0 − 3

f(0) = 0 − 3

f(0) = −3

### Answer:

The y-intercept of **f(x) = 2x − 3** is **−3**.

## Another Real Example of How to Find the Y-intercept of a Function

### Question

What is the y-intercept of the function **f(x) = x ^{2} + 4x + 2**?

### Step-by-Step:

# 1

Write the function. This is a quadratic equation.

f(x) = x^{2} + 4x + 2

**Note:** x^{2} = x × x (x squared) **and** 4x = 4 × x.

# 2

Substitute **x = 0** into the function.

f(0) = 0^{2} + 4 × 0 + 2

f(0) = 0 × 0 + 4 × 0 + 2

f(0) = 0 + 0 + 2

f(0) = 2

### Answer:

The y-intercept of **f(x) = x ^{2} + 4x + 2** is

**2**.