Question

The vertex of this parabola is at (-4, -1). When the y-value is 0, the x-value is 2. What is the coefficient of the squared term in the parabola's equation?

A. -3
B. 3
C. -6
D. 6

Answer 1

the coefficient of the squared term for this parabola is 6

Explanation:

Answer 2

For this question, we'll need the vertex form of a parabola, which, for a quadratic function, is:



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

where (h,k) is the vertex of the parabola. In this case, our parabola is opening horizontally to the right, so we need to swap the x and y in our equation. We have:


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

We've been given a the coordinates of the vertex (-4,-1) as well as the coordinates for a point on the parabola (2,0), so we can substitute in the values from both of these coordinates to easily solve for a, the coefficient of the squared term.


`h=-4\\k=-1\\x=2\\y=0\\\\2=a(0-(-1))^2+(-4)\\2=a(1)^2-4\\2=a-4\\6=a`

So, the coefficient of the squared term for this parabola is 6.