1. **State the problem:** Write the quadratic function $f(x) = x^2 + 2x - 4$ in vertex form. 2. **Recall the vertex form formula:** The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex of the parabola. 3. **Complete the square:** Start with the given function: $$f(x) = x^2 + 2x - 4$$ Group the $x$ terms: $$f(x) = (x^2 + 2x) - 4$$ To complete the square, take half of the coefficient of $x$, which is $2$, half is $1$, and square it: $1^2 = 1$. Add and subtract $1$ inside the parentheses: $$f(x) = (x^2 + 2x + 1 - 1) - 4$$ Rewrite the perfect square trinomial: $$f(x) = ((x + 1)^2 - 1) - 4$$ Simplify: $$f(x) = (x + 1)^2 - 5$$ 4. **Interpretation:** The vertex form is $$f(x) = (x + 1)^2 - 5$$ which means the vertex is at $(-1, -5)$. 5. **Answer:** The correct vertex form is $(x + 1)^2 - 5$. --- **Final answer:** $f(x) = (x + 1)^2 - 5$