Question

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?

Answer 1

Answer:

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:

$4p(y-k)=(x-h)^2$

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:

$4p(6-5)=(-1-3)^2$

which simplifies to

$4p(1)=(-4)^2$ and

4p = 16 so

p = 4

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

$4(4)(y-5)=(x-3)^2$ and

$16(y-5)=(x-3)^2$

We divide both sides by 16 to get

$y-5=\frac{1}{16}(x-3)^2$ and to finish it off properly:

$y=\frac{1}{16}(x-3)^2+5$

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

Answer 2

Answer:

The correct answer is -4.

Step-by-step explanation: