[tex]f(x)=-(x-1)^2+4[/tex]
(a)
This is a parabola which has a vertex located at (1,4). Since the leading coefficient is negative, it opens downwards. So:
(b)
As we can see:
[tex]\begin{gathered} \lim _{x\to-\infty}f(x)=-\infty \\ \lim _{x\to\infty}f(x)=-\infty \end{gathered}[/tex]
In both cases, the function tends to -∞.
(c)
We can find these coordinates evaluating the function for x = 0, so:
[tex]\begin{gathered} f(0)=-(0-1)^2+4 \\ f(0)=-1+4 \\ f(0)=3 \\ so\colon \\ P=(0,3) \end{gathered}[/tex]
