Question: Question 5
What is the vertex of $p(x) = (x + 2)^2 - 5$?
Option A
$(-2, -5)$
Option B
$(2, -5)$
Option C
$(-2, 5)$
Option D
$(2, 5)$
1. **State the problem:** Find the vertex of the quadratic function $$p(x) = (x + 2)^2 - 5$$.
2. **Recall the vertex form of a quadratic:** A quadratic function in vertex form is $$p(x) = a(x - h)^2 + k$$ where $$(h, k)$$ is the vertex.
3. **Identify $h$ and $k$ from the given function:** Here, $$p(x) = (x + 2)^2 - 5$$ can be rewritten as $$p(x) = (x - (-2))^2 - 5$$.
4. So, $$h = -2$$ and $$k = -5$$.
5. **Therefore, the vertex is** $$(-2, -5)$$.
6. **Answer:** Option A $(-2, -5)$.