Answer:
The correct option is D. [tex]y=(x-2)^{2}-5[/tex]
Step-by-step explanation:
If the vertex V of the parabola has the following coordinates :
[tex]V=(xV,yV)[/tex]
One way to write the equation of the parabola is :
[tex]y=a(x-xV)^{2}+yV[/tex]
Where xV and yV are the coordinates from the vertex of the parabola and ''a'' is a real number.
If [tex]a>0[/tex] ⇒ The parabola is concave upward
If [tex]a<0[/tex] ⇒ The parabola is concave downward
In this exercise
[tex]V=(xV,yV)=(2,-5)[/tex] ⇒
One way to write this parabola is
[tex]y=a(x-2)^{2}-5[/tex]
The graph of the parabola is concave upward ⇒[tex]a>0[/tex]
The option D. is
[tex]y=1(x-2)^{2}-5[/tex] Where [tex]a=1[/tex] and [tex]1>0[/tex] ⇒
The correct option is D.
