Answer:
[tex]f(x) = (x+1)^{2} + 2[/tex]
Step-by-step explanation:
In order to change a quadratic equation to vertex form, you can follow these steps:
quadratic form: [tex]f(x) = x^{2} +2x +3[/tex]
Transfer 3 to the other side of the equation, so add -3 to both sides of the equation and simplify.
[tex]f(x) -3 = x^{2} +2x +3 - 3[/tex]
[tex]f(x) -3 = x^{2} +2x[/tex]
Now if you look at the expression if you add 1 to both sides of the equation you will complete the perfect square trinomial
[tex]f(x) -3 + 1 = x^{2} +2x + 1[/tex]
[tex]f(x) - 2 = x^{2} +2x + 1[/tex]
Write the trinomial factors:
[tex]f(x) - 2 = (x + 1)(x + 1) ---> f(x) + 2 = (x^{2} + 1)^{2}[/tex]
Finally simplify, clear f(x)
[tex]f(x) = (x^{2} + 1)^{2} + 2[/tex]
Now it has the form [tex]f(x) = a(x -h)^{2} + k[/tex]
then (h, k) will be = (-1, 2)
