Question

question
what is the y - intercept of the polynomial $f(x)$ defined below? write the y - value only.
$f(x)=-4x^{2}-2x^{6}-x^{3}-7x^{4}$

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( f(x) \) is the value of \( f(x) \) when \( x = 0 \). So we need to substitute \( x = 0 \) into the polynomial \( f(x)=- 4x^{2}-2x^{6}-x^{3}-7x^{4} \).

Step2: Substitute \( x = 0 \) into the polynomial

When \( x = 0 \), we have:
\( f(0)=-4(0)^{2}-2(0)^{6}-(0)^{3}-7(0)^{4} \)
Since any non - zero number raised to the power of 0 is 1, but 0 raised to any positive power is 0. So \( (0)^{2}=0 \), \( (0)^{6}=0 \), \( (0)^{3}=0 \), \( (0)^{4}=0 \).
Then \( f(0)=-4\times0 - 2\times0-0 - 7\times0=0 \)

Answer:

0