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

f(x)=(4x^(2)-5)(2x+4)(x^(2)-1)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=\left(4 x^{2}-5\right)(2 x+4)\left(x^{2}-1\right)$ $\newline$ Answer:

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Find the roots of factored polynomials

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=\left(4 x^{2}-5\right)(2 x+4)\left(x^{2}-1\right)

\newline

Answer:

Evaluate $f(x)$ at $x=0$ : To find the $y$ -coordinate of the $y$ -intercept of the polynomial function $f(x)$ , we need to evaluate $f(x)$ when $x = 0$ . This is because the $y$ -intercept occurs where the graph of the function crosses the $y$ -axis, and the $x$ -coordinate is always $x=0$ $0$ at the $y$ -axis.
Substitute $x=0$ into $f(x)$ : Let's substitute $x = 0$ into the function $f(x) = (4x^2 - 5)(2x + 4)(x^2 - 1)$ . $\newline$ $f(0) = (4(0)^2 - 5)(2(0) + 4)(0^2 - 1)$
Simplify the expression: Now we simplify the expression by calculating the value of each term with $x = 0$ . $f(0) = (0 - 5)(0 + 4)(0 - 1)$
Further simplify the expression: Further simplifying the expression, we get: $f(0) = (-5)(4)(-1)$
Calculate y-coordinate: Multiplying the numbers together gives us the y-coordinate of the y-intercept. $\newline$ $f(0) = 20$

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