What is the equation of the parabola shown in the graph?

ANSWER[tex]{(y + 2)}^{2} = 8(x - 4)[/tex]EXPLANATIONThe given parabola has equation of the form[tex] {(y - k)}^{2} = 4p(x - h)[/tex]where (h,k) is the vertex of the parabola.The vertex of the given parabola is (4,-2).and p is the distance between the foci and the vertex.[tex] |p| = 2[/tex]The parabola opens towards the positive x-axis, therefore p=2.Hence the equation of the parabola is [tex] {(y + 2)}^{2} = 4 \times 2(x - 4)[/tex][tex]{(y + 2)}^{2} = 8(x - 4)[/tex]