Answer:
Option 4 is the correct answer.
Step-by-step explanation:
There are four equations of a parabola given in the question and we have to find the equation for which axis of symmetry is x = +2
Since line of symmetry of a parabola passes through its vertex so will find - Vertex of all the equations.
(1) [tex]y=x^{2}+4x-2[tex]
[tex]y=x^{2}+4x+4-6[/tex]
[tex]=(x+2)^{2}-6[/tex]
So vertex is ( -2, -6 )
(2) [tex]y=x^{2}-4=(x-0)^{2} -4[/tex]
Vertex is ( 0, -4 )
(3) [tex]y=x^{2} -2[/tex]
[tex]y=(x-0)^{2} -2[/tex]
vertex is ( 0, -2 )
(4) [tex]y=x^{2} -4x+2[/tex]
=[tex]x^{2} -4x+4-2[/tex]
=[tex](x-2)^{2}-2[/tex]
So vertex will be ( +2, -2 )
Out of all equations we find vertex of equation (4) is x=2 and y=-2, so line of symmetry will be x=2.
Option 4 is the correct answer.
