- Problem 1: The vertex of the parabola is at (0, -1). The standard form for a vertical shift is f(x) = x² + k. Since the vertex is shifted down by 1 unit from the origin, k = -1. Therefore, the equation is f(a) = a² - 1.
- Problem 2: The vertex of the parabola is at (0, 5). The standard form for a vertical shift is f(x) = x² + k. Since the vertex is shifted up by 5 units from the origin, k = 5. Therefore, the equation is f(z) = z² + 5.
- Problem 3: The vertex of the parabola is at (-2, -1). The standard form for a horizontal and vertical shift is f(x) = (x - h)² + k. Here, h = -2 and k = -1. However, none of the options include a vertical shift. Looking again, if we assume the vertex is at (-2, 0), then h = -2 and k = 0, giving f(n) = (n + 2)². This matches the graph’s shape and horizontal position. The red dot appears to be at (-2, 0) based on the grid. So, the correct equation is f(n) = (n + 2)².
- Problem 4: The vertex of the parabola is at (-9, 0). The standard form for a horizontal shift is f(x) = (x - h)². Here, h = -9, so the equation is f(m) = (m + 9)².
Parent Tip: Review the logic above to help your child master the concept of function transformations worksheet answers.
