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

Question

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

UpStudy AI · Accepted Answer

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!
- **Vertex of $$ f(x) $$**: $$(-2, 0)$$ - **AOS of $$ f(x) $$**: $$ x = -2 $$ - **Vertex of $$ h(x) $$**: $$(5, 0)$$

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

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions