When we talk about vertical shifts in quadratic functions, we are looking at how moving a U-shaped graph called a parabola up or down changes its picture.

A quadratic function usually looks like this:

y = ax² + bx + c

Here, the c value helps us find out where the top point of the parabola is located on the y-axis.

How Vertical Shifts Work

1. Shifting Upward: When you add a positive number to c, the whole graph goes up. For example, if we start with y = x² and change it to y = x² + 3, the highest point (or vertex) of the parabola moves from (0,0) to (0,3). That means it goes up by 3 units.

2. Shifting Downward: If you take away a positive number from c, the graph shifts down. For example, changing y = x² to y = x² - 2 makes the vertex move down to (0,-2). So it goes down by 2 units.

Visual Impact

• Vertex Location: The y-coordinate of the vertex changes, which affects the highest or lowest point of the parabola.
• Intercepts: The x-intercepts, where the graph crosses the x-axis, might also change when we shift the graph up or down because they depend on the value of c.

This transformation is important because it helps us see how algebra connects to the visual shapes of parabolas in graphing. Understanding these shifts is key to effectively graphing and working with quadratic functions!