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

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

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

\newline

Answer:

Evaluate Function at $x=0$ : To find the $y$ -coordinate of the $y$ -intercept of the function $f(x)$ , 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 $0$ . $\newline$ Calculation: $y$ $0$
Substitute $x=0$ : Now we substitute $x=0$ into the function and simplify. $\newline$ Calculation: $f(0) = -(1)(-4)^2 = -(1)(16) = -16$
Find Y-Coordinate: The $y$ -coordinate of the $y$ -intercept is the value we found by substituting $x=0$ into the function, which is $-16$ .

More problems from Reflections of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

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

\newline

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

\newline

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

\newline

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

Posted 9 months ago

Question

What does the transformation

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\text{translates it } 4 \text{ units right}

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\text{translates it } 4 \text{ units down}

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\text{translates it } 4 \text{ units left}

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\text{translates it } 4 \text{ units up}

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Question

What does the transformation

f(x) \mapsto f(4x)

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[A] stretches it vertically

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[B] stretches it horizontally

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[C]shrinks it horizontally

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[D]shrinks it vertically

Posted 8 months ago

Question

g(x)

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g(x) = 10x - 82

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g(x) = 10x + 98

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g(x) = 10x - 1

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g(x) = 10x + 17

Posted 9 months ago

Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

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\text{[D]translation 10 units right}

Posted 8 months ago

Question

y=x^{2}

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. What is the equation of the new parabola?

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y=

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Question

y=x^{2}

is shifted down by

6

units and to the right by

5

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What is the equation of the new parabola?

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Question

y=x^{2}

is shifted up by

2

units and to the right by

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What is the equation of the new parabola?

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Question

y=x^{2}

is reflected across the

x

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What is the equation of the new parabola?

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y=\square

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Question

y=x^{2}

is scaled vertically by a factor of

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What is the equation of the new parabola?

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y=

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