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

1/16

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=(1)/(16)(x-3)^2` and to finish it off properly:

`y=(1)/(16)(x-3)^2+5`

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

Answer 2

The correct answer is -4.

Explanation: