Find the y-intercept of the polynomial function.
-$$f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$$
A) $- 36$
B) 36
C) $- 18$
D) 18 Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.

Question

Quizplus · Accepted Answer

DThe y-intercept of a polynomial function is found by evaluating the function at $x = 0$. Substituting $x = 0$ into the given function, we get $f(0) = (0 - 2)^2(0^2 - 9) = 4(-9) = -36$, which corresponds to choice A.To determine the symmetry of the graph, we observe that the given polynomial is not an even function (since it does not satisfy $f(x) = f(-x)$ for all $x$) and it is not an odd function (since it does not satisfy $f(-x) = -f(x)$ for all $x$). Therefore, the graph has neither y-axis symmetry nor origin symmetry, which corresponds to choice D.

Find the Y-Intercept of the Polynomial Function f(x)=(x−2)2(x2−9)f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)f(x)=(x−2)2(x2−9)

Find the Y-Intercept of the Polynomial Function $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$