**Quadratic equations** are mathematical functions where one of the x variables is squared, or taken to the second power like this: **x ^{2}**. When these functions are graphed, they create a parabola which looks like a curved "U" shape on the graph. This is why a quadratic equation is sometimes called a parabola equation.

Two important values concerning these mathematical functions are the x-intercept and the y-intercept. The **x-intercept** indicates where the parabola graph of that function crosses the x axis. There can be one or two x intercepts for a single quadratic equations.

The **y-intercept** indicates where the parabola crosses the y axis. There is only one y intercept for each quadratic equation.

## What Is the y Intercept of a Quadratic Function?

The y-intercept is where the parabola of a function crosses (or intercepts) the y axis. Another way to define the y-intercept is the value of y when x is equal to zero.

Because the y intercept is a point on a graph, you'll usually write it in point/coordinate form. For example, let's say your y value of the y intercept is 6.5. You would write the y intercept as **(0, 6.5)**.

## Different Forms of Quadratic Equations

Quadratic equations come in three general forms. These are the standard form, vertex form and factored form.

**Standard form** looks like this:

**y = ax ^{2} + bx + c** where a, b and c are known constants and x and y are variables.

**Vertex form** looks like this:

**y = a(x + b) ^{2} + c** where a, b and c are known constants and x and y are variables.

**Factored form** looks like this:

**y = a(x + r _{1})(x + r_{2})** where a is a known constant, r

_{1}and r

_{2}are "roots" of the equation (x intercepts), and x and y are variables.

Each of the forms looks drastically different, but the method for finding the y intercept of a quadratic equation is the same despite the various forms.

## How to Find the Y Intercept of a Quadratic in Standard Form

Standard form is perhaps the most common and the easiest to understand. Simply plug zero (0) in as the value of x in the standard quadratic equation and solve. Here's an example.

Let's say your function is **y = 5x ^{2} + 11x + 72**. Assign "0" as your x value and solve.

y = 5(0)^{2} + 11(0) + 72 **= 72**

You would then write the answer in the coordinate form of **(0, 72)**.

## How to Find the Y Intercept of a Quadratic in Vertex Form

As with standard form, simply plug "0" in as the value of x and solve. Here's an example.

Let's say your function is **y = 134(x + 56) ^{2} - 47.** Assign "0" as your x value and solve.

y = 134(0 + 56)^{2} - 47 = 134(0)^{2} - 47 **= -47**

You would then write the answer in the coordinate form of **(0, -47)**.

## How to Find the Y Intercept of a Quadratic in Factored Form

Lastly, you have factored form. Again, you simply plug "0" in as the value of x and solve. Here's an example.

Let's say your function is **y = 7(x - 8)(x + 2)**. Assign "0" as your x value and solve.

y = 7(0-8)(0+2) = 7(-8)(2) **= -112**

You would then write the answer in the coordinate form of **(0, -112)**.

## A Quick Trick

With both standard and vertex form, you may have noticed that the y-intercept value is equal to the value of the **c** constant in the equation itself. That is going to be true with every parabola/quadratic equation you encounter in those forms.

Simply look for the c constant and that is going to be your y-intercept. You can double check by using the x value of zero method.

References

- Math Is Fun: Quadratic Equations
- Kendall Hunt Education: Factored Form
- California State University Northridge: Parabolas
- New Paltz Central School District: Quadratic Equations in Three Forms
- ThoughtCo: How to Find the Y-Intercept of a Parabola
- University of Georgia: The Quadratic Function
- Lumen Learning: Intercepts of Quadratic Functions

About the Author

Elliot Walsh holds a B.S in Cell and Developmental Biology and a B.A in English Literature from the University of Rochester. He's worked in multiple academic research labs, at a pharmaceutical company, as a TA for chemistry, and as a tutor in STEM subjects. He's currently working full-time as a content writer and editor.