The vertex of this parabola is at (3, 5). when the y-value is 6, the x-value is -1. what is the coefficient of the squared term in the parabola's equation?

1/16

Step-by-step explanation:

If you plot the vertex and the point, you'll find that the point lies above the vertex, thus, the parabola opens upwards, so the vertex form of this parabola will be:

In order to solve for the leading coefficient, we first need to solve for p.  We will fill in the vertex form with all the info we have:

which simplifies to

and

4p = 16 so

p = 4

Now we can rewrite the parabola using this value of p:

and

We divide both sides by 16 to get

and to finish it off properly:

As you can see, the leading coefficient is 1/16