ANSWER
The y-intercept is
[tex](0,1)[/tex]
EXPLANATION
The given polynomial function is
[tex]f(x) = - {x}^{3} + 3 {x}^{2} + 1[/tex]
At y-intercept the value of x is zero.
Therefore we need to put
[tex]x = 0[/tex]
into the given polynomial function to determine the corresponding y-value.
[tex]f(0) = - {(0)}^{3} + 3 {(0)}^{2} + 1[/tex]
This will give us,
[tex]f(0) = 0 + 0+ 1[/tex]
We further simplify to obtain,
[tex]f(0) =1[/tex]
This means that when
[tex]x = 0[/tex]
the value of the function is
[tex]1[/tex]
Hence the y-intercept is
[tex](0,1)[/tex]
