Answer:
1) [tex]y=(x-1)^2+4[/tex]
2) [tex]y=-2(x+1)^2-9[/tex]
Step-by-step explanation:
The equation of the parabola in the vertex form is
[tex]y=a(x-h)^2+k,[/tex]
where [tex](h,k)[/tex] is the vertex of the parabola.
1) Given:
[tex]y= x^2-2x+5[/tex]
Rewrite it as
[tex]y=x^2-2x+1+4\\ \\y=(x-1)^2+4[/tex]
2) Given:
[tex]y= -2x^2-4x-11[/tex]
Rewrite it as
[tex]y=-2x^2-4x-2-9\\ \\y=-2(x^2+2x+1)-9\\ \\y=-2(x+1)^2-9[/tex]
