# Quadratic Function - Parent Function and Vertical Shifts

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

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## Common Traits of Quadratic Functions

• 1 vertex
• 1 line of symmetry
• The highest degree (the greatest exponent) of the function is 2
• The graph is a parabola

## Parent and Offspring

The equation for the quadratic parent function is

y = x2, where x ≠ 0.

Here are a few quadratic functions:

• y = x2 - 5
• y = x2 - 3x + 13
• y = -x2 + 5x + 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.

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## Vertical Translations: Upward and Downward

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

y = x2 + 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

1. Add c, and the graph will shift up from the parent c units.
2. Subtract c, and the graph will shift down from the parent c units.
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## 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 = x2 + 1 is (0,1).

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## 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 = x2 - 1 is (0,-1).

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## Example 3: Make a Prediction

How does y = x2 + 5 differ from the parent function, y = x2?

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