A **parent function** is a template of domain and range that extends to other members of a function family.

## Common Traits of Quadratic Functions

## Parent and Offspring

The equation for the quadratic parent function is

y=x^{2}, wherex≠ 0.

Here are a few quadratic functions:

*y*=*x*^{2}- 5*y*=*x*^{2}- 3*x*+ 13*y*= -*x*^{2}+ 5*x*+ 3

The children are transformations of the parent. Some functions will shift upward or downward, open wider or more narrow, boldly rotate 180 degrees, or a combination of the above. This article focuses on vertical translations. Learn why a quadratic function shifts upward or downward.

## Vertical Translations: Upward and Downward

You can also look at a quadratic function in this light:

y=x^{2}+c, x ≠0

When you start with the parent function, *c* = 0. Therefore, the vertex (the highest or lowest point of the function) is located at (0,0).

## Quick Translation Rules

- Add
*c*, and the graph will shift up from the parent*c*units. - Subtract
*c*, and the graph will shift down from the parent*c*units.

## Example 1: Increase c

When 1 is **added **to the parent function, the graph sits 1 unit **above **the parent function.

The vertex of *y* = *x*^{2} + 1 is (0,1).

## Example 2: Decrease c

When 1 is **subtracted **from the parent function, the graph sits 1 unit **below **the parent function.

The vertex of *y* = *x*^{2} - 1 is (0,-1).

## Example 3: Make a Prediction

How does *y* = *x*^{2} + 5 differ from the parent function, *y* = *x*^{2}?

## Example 3: Answer

The function, *y* = *x*^{2} + 5 shifts 5 units upward from the parent function.

Notice that the vertex of *y* = *x*^{2} + 5 is (0,5), while the vertex of the parent function is (0,0).