Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

In vertex form, what does the variable "h" represent?

1. Vertical shift

2. Horizontal shift

3. Y-intercept

4. Missing angle

The correct answer is: Horizontal shift

In vertex form, which is typically expressed as \( y = a(x - h)^2 + k \), the variable \( h \) represents the horizontal shift of the parabola. This means that the entire graph is shifted left or right on the coordinate plane depending on the value of \( h \). If \( h \) is positive, the graph shifts to the right, and if \( h \) is negative, the graph shifts to the left. This characteristic of \( h \) is crucial in understanding how the graph is positioned relative to the standard position of the parabola. In contrast, other parameters in vertex form have different roles; for instance, \( k \) denotes the vertical shift, which moves the graph up or down. The y-intercept, mentioned in one of the other options, describes where the graph crosses the y-axis, but it is not determined by the \( h \) value. Therefore, identifying \( h \) as the horizontal shift is key in graphing and analyzing parabolic functions in their vertex form.