Question

What is the y-intercept of f(x)=-X^3+3x^2+1?

Answer 1

ANSWER

The y-intercept is

$(0,1)$


EXPLANATION

The given polynomial function is


$f(x) = - {x}^{3} + 3 {x}^{2} + 1$

At y-intercept the value of x is zero.


Therefore we need to put
$x = 0$

into the given polynomial function to determine the corresponding y-value.



$f(0) = - {(0)}^{3} + 3 {(0)}^{2} + 1$

This will give us,


$f(0) = 0 + 0+ 1$

We further simplify to obtain,
$f(0) =1$



This means that when
$x = 0$
the value of the function is
$1$

Hence the y-intercept is

$(0,1)$