Answer:
(-2, 1)
Step-by-step explanation:
The vertex (h, k) of a parabola of the form [tex]ax^{2}+bx+c[/tex] is found by the formula [tex]h=\frac{-b}{2a}[/tex], and then evaluating the parabola at [tex]x=h[/tex] to find [tex]k[/tex].
We know from our parabola that [tex]a=1[/tex] and [tex]b=4[/tex], so let's find [tex]h[/tex]:
[tex]h=\frac{-b}{2a}[/tex]
[tex]h=\frac{-4}{2(1)}[/tex]
[tex]h=\frac{-4}{2}[/tex]
[tex]h=-2[/tex]
Now, we just need to evaluate our function at [tex]x=h[/tex] to find [tex]k[/tex]. In other words, we just need to replace [tex]x[/tex] with -2 and simplify:
[tex]k=(-2)^{2} +4(-2)+5[/tex]
[tex]k=4-8+5[/tex]
[tex]k=1[/tex]
We can conclude that the vertex of our parabola is (-2, 1)
