A parabola has a vertex of \( (-4,-1) \) and a y-intercept of 10 . Identify the correct equation of the parabola in vertex form. Select one: \( \begin{array}{l}y=10 / 17(x+1)-4 \\ y=10 / 17(x+4)^{2}-1 \\ y=11 / 16(x+4)^{2}-1 \\ y=10 / 17(x+1)^{2}-4\end{array} \)

To find the equation of the parabola in vertex form, we can start with the vertex form of a parabola given by: \[ y = a(x - h)^2 + k \] where \((h, k)\) is the vertex. For this parabola, the vertex is \((-4, -1)\), so we have: \[ y = a(x + 4)^2 - 1 \] Next, we need to find the value of \(a\). We know the y-intercept is 10, which means when \(x = 0\), \(y = 10\). Plugging in the y-intercept: \[ 10 = a(0 + 4)^2 - 1 \] \[ 10 = 16a - 1 \] \[ 11 = 16a \] \[ a = \frac{11}{16} \] Now substituting \(a\) back into the vertex form, we get: \[ y = \frac{11}{16}(x + 4)^2 - 1 \] Thus, the correct equation of the parabola in vertex form is: \[ y = \frac{11}{16}(x + 4)^2 - 1 \] So, the correct answer is \( y=11 / 16(x+4)^{2}-1 \).