C. \( f(x) \equiv(x+2)^{2} \) Enter the numbers. Click on "Submit" to check your work. Translates \( \begin{array}{l}\text { vertex } \\ \text { AOS: } \\ \text { d. } h(x) \equiv(x-5)^{2}\end{array} \)

To translate the function \( f(x) \equiv (x+2)^{2} \) into the vertex form of a parabola and find the vertex, axis of symmetry (AOS), and the function \( h(x) \equiv (x-5)^{2} \), we can follow these steps: 1. **Identify the vertex of \( f(x) \)**: The vertex form of a parabola is given by \( f(x) = a(x-h)^2 + k \), where \( (h, k) \) is the vertex. For \( f(x) = (x+2)^2 \), we can rewrite it as: \[ f(x) = (x - (-2))^2 + 0 \] Thus, the vertex \( (h, k) \) is \( (-2, 0) \). 2. **Determine the axis of symmetry (AOS)**: The axis of symmetry for a parabola in vertex form is given by the line \( x = h \). Therefore, for \( f(x) \): \[ \text{AOS: } x = -2 \] 3. **Translate to \( h(x) \)**: The function \( h(x) \equiv (x-5)^2 \) has its vertex at \( (5, 0) \). Now, let's summarize the results: - **Vertex of \( f(x) \)**: \( (-2, 0) \) - **AOS of \( f(x) \)**: \( x = -2 \) - **Vertex of \( h(x) \)**: \( (5, 0) \) If you need to enter these values, they would be: - Vertex: \((-2, 0)\) - AOS: \(-2\) Please let me know if you need any further calculations or clarifications!