Question

The vertex of this parabola is at (-2, 1). Which of the following could be itsequation?5(-2,1)A. x = 4(y- 1)2-2B. y = 4(x - 2)2 + 1c. y = 4(x - 2)2-1D. x = 4(y + 1)2-2

Answer 1

A parabola can be written in the vertex form as follows:

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

Where:

$(h,k)$

Are the coordinates of the vertex.

Since the vertex is at:

$\begin{gathered} (h,k)=(-2,1) \\ \end{gathered}$

The equation is:

$\begin{gathered} y=a(x-(-2))^2+1 \\ y=a(x+2)+1 \end{gathered}$

But, since it is a horizontal parabola:

$\begin{gathered} x=a(y-k)+h \\ so\colon \\ x=a(y-1)^2-2 \end{gathered}$

Therefore, the only valid option is:

$x=4(y-1)^2-2$