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

Which statement is true if there is no value for "a" in the vertex form of a parabola?

1. Go over 1, up 1

2. Go over 2, down 4

3. Graph the y-intercept

4. Change the vertex to (0,0)

The correct answer is: Go over 1, up 1

When we consider the vertex form of a parabola, which is typically expressed as \(y = a(x - h)^2 + k\), the parameter "a" plays a significant role in determining the shape and direction of the parabola. If there is no value assigned to "a," it can be interpreted that "a" equals 1 by default in the context of the basic vertex form. In this case, the parabola opens upwards and has a vertex at the point (h, k). The vertex form allows us to visualize the transformation of the standard parabola \(y = x^2\). Without scaling or reflection caused by "a," the parabola maintains its standard behavior. The statement that accurately describes the movement of the graph starting from the vertex when "a" is presumed to be 1 is represented by the pattern of going over 1 unit in the x-direction and up 1 unit in the y-direction from the vertex. This indicates the parabolic growth in its typical form, as the slope of the tangent to the parabola at the vertex is 0, and it increases at a rate of 1. Understanding this movement is crucial in graphing the parabola accurately, especially when plotting points based