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: $$ \begin{array}{l}y=10 / 17(x+1)-4 \ y=10 / 17(x+4)^{2}-1 \ y=11 / 16(x+4)^{2}-1 \ y=10 / 17(x+1)^{2}-4\end{array} $$

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To find the correct equation of the parabola in vertex form, we start with the vertex form of a parabola, which is given by:

$$
y = a(x - h)^2 + k
$$

where $$(h, k)$$ is the vertex of the parabola. In this case, the vertex is $$(-4, -1)$$, so we have:

$$
y = a(x + 4)^2 - 1
$$

Next, we need to determine the value of $$a$$. We can use the y-intercept of the parabola, which is given as 10. The y-intercept occurs when $$x = 0$$. Substituting $$x = 0$$ into the equation gives us:

$$
10 = a(0 + 4)^2 - 1
$$

Now, we can solve for $$a$$:

$$
10 = a(4^2) - 1
$$
$$
10 = 16a - 1
$$
$$
10 + 1 = 16a
$$
$$
11 = 16a
$$
$$
a = \frac{11}{16}
$$

Now we can substitute $$a$$ back into the vertex form equation:

$$
y = \frac{11}{16}(x + 4)^2 - 1
$$

Now, let's compare this with the provided options:

1. $$ y = \frac{10}{17}(x + 1) - 4 $$
2. $$ y = \frac{10}{17}(x + 4)^{2} - 1 $$
3. $$ y = \frac{11}{16}(x + 4)^{2} - 1 $$
4. $$ y = \frac{10}{17}(x + 1)^{2} - 4 $$

The correct equation of the parabola in vertex form is:

$$
\boxed{y = \frac{11}{16}(x + 4)^{2} - 1}
$$

This corresponds to option 3.
The correct equation of the parabola in vertex form is $$ y = \frac{11}{16}(x + 4)^2 - 1 $$.

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: \( \begin{array}{l}y=10 / 17(x+1)-4 \\ y=10 / 17(x+4)^{2}-1 \\ y=11 / 16(x+4)^{2}-1 \\ y=10 / 17(x+1)^{2}-4\end{array} \)

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