- Problem 1: The vertex of the parabola is at (0, -1). The standard form for a parabola with vertex (h, k) is f(x) = (x - h)^2 + k. Substituting h=0 and k=-1 gives f(a) = (a - 0)^2 - 1, which simplifies to f(a) = a^2 - 1.
- Problem 2: The vertex of the parabola is at (0, 5). Using the vertex form f(x) = (x - h)^2 + k with h=0 and k=5 gives f(z) = (z - 0)^2 + 5, which simplifies to f(z) = z^2 + 5.
- Problem 3: The vertex of the parabola is at (-2, -1). Using the vertex form f(x) = (x - h)^2 + k with h=-2 and k=-1 gives f(n) = (n - (-2))^2 + (-1), which simplifies to f(n) = (n + 2)^2 - 1. However, this option is not listed. Looking at the options, f(n) = (n + 2)^2 has its vertex at (-2, 0), which does not match the graph. None of the given options correctly represent the graph shown in problem 3.
- Problem 4: The vertex of the parabola is at (-9, 0). Using the vertex form f(x) = (x - h)^2 + k with h=-9 and k=0 gives f(m) = (m - (-9))^2 + 0, which simplifies to f(m) = (m + 9)^2.
The correct answers are:
1. f(a) = a^2 - 1
2. f(z) = z^2 + 5
3. None of the provided options match the graph.
4. f(m) = (m + 9)^2
Parent Tip: Review the logic above to help your child master the concept of worksheet transformations of quadratic functions.
