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

f(x)=-x(5x+3)(x-4)^(2)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=-x(5 x+3)(x-4)^{2}$ $\newline$ Answer:

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Transformations of functions

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=-x(5 x+3)(x-4)^{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 $x = 0$ , 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 $0$ .
Substitute $x = 0$ : Substitute $x = 0$ into the function $f(x) = -x(5x+3)(x-4)^{2}$ . $\newline$ $f(0) = -0(5\cdot0+3)(0-4)^{2}$
Simplify expression: Simplify the expression by performing the multiplication and exponentiation. $\newline$ $f(0) = -0(0+3)(-4)^{2}$ $\newline$ $f(0) = -0(3)(16)$
Final result: Since any number multiplied by zero is zero, the entire expression simplifies to $0$ . $f(0) = 0$
Find y-intercept: The y-coordinate of the y-intercept is the value of $f(0)$ , which we have found to be $0$ .

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\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

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\text{}(B)g(x) = 9|x-2| - 4\text{]}

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Question

What kind of transformation converts the graph of

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Question

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Question

y=x^{2}

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What is the equation of the new parabola?

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