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Find the
y-coordinate of the
y-intercept of the polynomial function defined below.

f(x)=x(x-5)(x-3)(x-6)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=x(x-5)(x-3)(x-6)$ $\newline$ Answer:

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Multiply and divide complex numbers

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=x(x-5)(x-3)(x-6)

\newline

Answer:

Evaluate at $x = 0$ : To find the $y$ -coordinate of the $y$ -intercept of the function $f(x)$ , we need to evaluate $f(x)$ at $x = 0$ , because the $y$ -intercept occurs where the graph of the function crosses the $y$ -axis, and the $x$ -coordinate of any point on the $y$ -axis is $y$ $0$ .
Substitute $x = 0$ : Substitute $x = 0$ into the polynomial function $f(x) = x(x - 5)(x - 3)(x - 6)$ . $f(0) = 0 \times (0 - 5) \times (0 - 3) \times (0 - 6)$
Perform multiplication: Perform the multiplication to find the value of $f(0)$ . $\newline$ $f(0) = 0 \times (-5) \times (-3) \times (-6)$ $\newline$ $f(0) = 0$ $\newline$ Since any number multiplied by zero is zero, the entire expression evaluates to zero.
Find y-coordinate: The y-coordinate of the y-intercept is the value of $f(0)$ , which we have found to be $0$ .

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