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

f(x)=2x(3x+4)(2x+1)(2x-1)^(2)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=2 x(3 x+4)(2 x+1)(2 x-1)^{2}$ $\newline$ Answer:

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Reflections of functions

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=2 x(3 x+4)(2 x+1)(2 x-1)^{2}

\newline

Answer:

Evaluate at $x = 0$ : To find the $y$ -coordinate of the $y$ -intercept of the function, we need to evaluate the function at $x = 0$ . This is because the $y$ -intercept occurs where the graph of the function crosses the $y$ -axis, and the $x$ -coordinate is always $0$ at the $y$ -axis.
Substitute $x = 0$ : Substitute $x = 0$ into the function $f(x)$ to find the y-coordinate of the y-intercept. $\newline$ $f(x) = 2x(3x+4)(2x+1)(2x-1)^{2}$ $\newline$ $f(0) = 2\cdot 0\cdot (3\cdot 0+4)(2\cdot 0+1)(2\cdot 0-1)^{2}$
Simplify the expression: Simplify the expression by performing the multiplication and evaluating the powers. $\newline$ $f(0) = 2\cdot0\cdot(0+4)(0+1)(0-1)^{2}$ $\newline$ $f(0) = 2\cdot0\cdot4\cdot1\cdot(-1)^{2}$
Continue simplifying: Continue simplifying the expression. $\newline$ $f(0) = 0 \times 4 \times 1 \times 1$ $\newline$ $f(0) = 0$
Final 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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