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Vertical Shift: Definition & Examples

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  • 0:01 What Is a Vertical Shift?
  • 1:21 Vertical Shift of a Point
  • 2:23 Vertical Shift of a…
  • 3:49 Vertical Shift of Parabola
  • 4:38 Lesson Summary
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Lesson Transcript
Instructor: Ellen Manchester
When graphing, a graph can be shifted up or down with very little work. In this lesson, we will be learning how to do a vertical shift. We will examine both the graphs of functions and the equations of the functions.

What Is a Vertical Shift?

When graphing any function or relation, the graph will always be a basic shape depending on the function. For instance, the function with a leading coefficient of x^2 will have a basic parabolic shape. The function involving an absolute value, will have a basic V-shape. Each function has a basic shape. This shape can be stretched, shrunk, shifted right or left, up or down, or flipped over. All of these shifts are called transformations. In this lesson, we will learn about the vertical shift.

A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens to the y-value of the graph. The y-axis of a coordinate plane is the vertical axis. When a function shifts vertically, the y-value changes. The x-value stays the same, while the y-value changes the amount of the shift. If it shifts up, then we add the value to the y-term. If it shifts down, we will subtract that value from the y-term.

Vertical Shift of a Point

Let's start with just a point on the coordinate plane. Let's start with the point A at (1,5). Remember when plotting a point, the address is written as an ordered pair (x,y). The x-value is read first, so you go right or left first, then up or down for the y-value. We plot the point A at 1 right, up 5 units. Now to create a vertical shift, let's move this point 5 units south or down.

Point
Vertical shift down

Notice the address to this new point A. The x-term remained the same, the y-term changed by 5. Since you moved down 5 units, you can see we just subtracted 5 from the y-term, (5 - 5 = 0). So the new point A' is (1,0).

Vertical Shift of a Linear Equation

Let's try a linear equation:

f(x) = 2x - 3

Remember, to graph a line, you put a point at the y-intercept, which is -3. From there the slope is the value next to the x variable. Count out the slope as rise/run. The slope, 2, equals 2/1 or rise 2, run 1.

Linear equation

Notice the two points on the line, (0,-3) and (1,-1), let's see what happens to these points when we shift this line up 3 units. Pay close attention to the y-value of the ordered pairs.

verticalshift line

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