Question

The vertex of the parabola below is at the point (3,2), and the point (4,6) ison the parabola. What is the equation of the parabola?O A. y= 4(x-3)2 + 2O B. y= 2(x - 2)2 + 3O c. x = 6(y - 3)2 + 2O D. y = 4(x+3)2 - 2

Answer 1

We have that the vertex form of the equation of the parabola is the following:

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

where (h,k) is the vertex of the parabola.

In this case, we have that the vertex is (h,k) = (3,2) and that the parabola passes through the point (x,y) = (4,6). Then, using the equation in vertex form, we have the following:

$\begin{gathered} (h,k)=(3,2) \\ (x,y)=(4,6) \\ \Rightarrow6=a(4-3)^2+2 \end{gathered}$

solving for 'a', we get:

$\begin{gathered} 6=a(4-3)^2+2 \\ \Rightarrow6-2=a(1)^2 \\ \Rightarrow a=4 \end{gathered}$

therefore, the equation of the parabola is:

$y=4(x-3)^2+2$