Answer:
[tex]\underline{\,\underline{\bold{(x+2)^2-13}}\,}[/tex]
Step-by-step explanation:
You can do it by completing the square:
[tex]x^2+4x-9\\\\\underbrace{x^2+4x+4}-4-9[/tex]
We add 4 to complete the square but we also subtract 4 because we don't want to change the equation (+4-4=0 so it doesn't change anything in equation)
[tex]x^2+4x+4=x^2+2\cdot x\cdot2+2^2[/tex]
so we get:
[tex]\underbrace{x^2+4x+4}-4-9\\\\{}\quad (x+2)^2-13[/tex]
The vertex is: (-2, -13)
(because x+2=x-h ⇒h=-2 and +q=-13 ⇒ q=-13)
We can also use that:
[tex]ax^2+bx+c=a(x-h)^2+k[/tex] for [tex]h=\frac{-b}{2a}\,,\quad k=ah^2+bh+c[/tex]
[tex]x^2+4x-9\quad\implies\quad a=1\,,\ b=4\\\\h=\frac{-4}{2\cdot1}=-\frac42=-2\\\\k=(-2)^2+4(-2)-9=4-8-9=-13\\\\a(x-h)^2+k\\\\1(x-(-2))^2+(-13)\\\\(x+2)^2-13[/tex]
