Question

The vertex of this parabola is at (2, -4). When the x-value is 3, the y-value is -1. What is the coefficient of the squared expression in the parabola's equation?

Answer 1

Hello,
As (2,-4) is the vertex, the parabola is y=k(x-2)²-4
As (3,-1,) is a point of the parabola:
-1=k*(3-2)²-4
==> k=3y=3(x-2)²-4 so, coefficient of x² is 3.

Answer 2

the coefficient of squared term in the parabola's equation is
`a = 3`

Explanation:

We are given the following information in the question:

Vertex of parabola: (2,-4)

Also, (x = 3, y = -1) lies on the parabola.

The general equation of parabola is of the form:

`y = a(x-h)^2 k \text{ where (h,k) is the vertex of the parabola}`

Putting h = 2, k = -4 in the equation, we get:

`y = a(x-2)^2-4\\y=a(x^2-4x+4)-4\\y = a(x^2 -4x + 4)-4`

Now, putting x = 3 and y = -1 in the above equation,we get:

`-1 = a(9-12+4) - 4\\-1 = a -4\\a = 4-1\\a = 3`

Hence, the coefficient of squared term in the parabola's equation is
`a = 3`