Question

The equations below are written in vertex form, y=a(x-h^2+k. In the parent function, a=1, h=0, and k=0. In the modified function, a=1, h=0, and k=2. Describe the effect of the parameter change on the modified graph. When k is 2, the graph shifts left 2 units. When k is 2, the graph shifts downward 2 units. When k is 2, the graph shifts right 2 units. When k is 2, the graph shifts upward 2 units.

Answer 1

d) When k is 2, the graph shifts upward 2 units.

Explanation:

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola. When a > 0 the parabola opens upward and the vertex is the minimum point. If a < 0 the parabola opens downward and the vertex is the maximum point.

In this case, the parent function has a = 1, h = 0, and k = 0, while the modified function has a = 1, h = 0, and k = 2. Since both functions have a positive 'a' value, they open upward, making their vertices minimum points.

Since the k-value of the vertex is its vertical coordinate, when we increase k by 2 units, it shifts the graph upward by 2 units.