For this question, we'll need the vertex form of a parabola, which, for a quadratic function, is:
[tex]y=a(x-h)^2+k[/tex]
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:
[tex]x=a(y-h)^2+k[/tex]
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.
[tex]h=-4\\k=-1\\x=2\\y=0\\\\2=a(0-(-1))^2+(-4)\\2=a(1)^2-4\\2=a-4\\6=a[/tex]
So, the coefficient of the squared term for this parabola is 6.
