Question

write y = x² + 4x - 1 in vertex form.

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. Given $y=x^{2}+4x - 1$.
We complete the square. For the quadratic expression $x^{2}+bx$, we add and subtract $(\frac{b}{2})^{2}$. Here $b = 4$, so $(\frac{b}{2})^{2}=4$.
$y=x^{2}+4x - 1=(x^{2}+4x+4)-4 - 1$.

Step2: Factor the perfect - square trinomial

$x^{2}+4x + 4=(x + 2)^{2}$, so $y=(x + 2)^{2}-5$.

Answer:

$y=(x + 2)^{2}-5$