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o-na [289]
3 years ago
7

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

Mathematics
1 answer:
marishachu [46]3 years ago
6 0

Answer:

\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18

Step-by-step explanation:

We have been given the function

f(x)=-2x^2+4x^3+3x^2+18

From the rational zeros theorem, we have

\text{Possible rational zeros}=\pm\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}

From the given function,

Leading coefficient = 2

Factors of 2 are 1,2

Constant term = 18

Factors of constant term = 1, 2, 3, 6, 9, 18

Hence, we have

\text{Possible rational zeros}=\pm\frac{1,2,3,6,9,18}{1,2}\\\\\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18

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Determine the Vertex of the following absolute value function.
prisoha [69]

Answer:

vertex = (-4, 5)

Step-by-step explanation:

In general, the graph of the absolute value function f(x) = a|x - h| + k will have its lowest value when f(x) = k  (or highest value for f(x) = -a|x - h| + k).  The lowest/highest value is the vertex (turning point).

Therefore, from inspection of the equation we can say that the y-coordinate of the vertex is 5.

Set the equation to 5 and then solve for x:

⇒ 5 = 1/2 |-X – 4| + 5

⇒ 1/2 |-X – 4| = 0

⇒ |-X – 4| = 0

Therefore, (-X - 4) = 0  and -(-X - 4) = 0

⇒ X = -4 (for both)

So the vertex is (-4, 5)

<u>Translations</u>

Absolute value parent function:  f(x) = | -x |

Horizontal translation left 4 units:  f(x) = |-x - 4|

Horizontal stretch of sf 1/2:  f(x) = 1/2 |-x - 4|

Vertical translation up 5 units:  f(x) = 1/2 |-x - 4| + 5

6 0
2 years ago
How do you know when there are no solutions to a system of equations?
Allushta [10]
No solution
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The lines are parallel
eg
y = 2x + 3; y = 2x + 5

Infinite solutions
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When one equation reduces to the second one.
2y = 10x + 6
y = 5x + 3 When you divide the first one by 2, you get the second one.
4 0
3 years ago
Please help me on my composition of functions homework
OlgaM077 [116]

Hey! This seems kinda hard. I really wish i could help but i cant understand it. I would ask my sister who is a math teacher to help u out! Just give me a like and a thumbs up so i can earn points please!?

7 0
3 years ago
Can some one help me plz
Olenka [21]

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1b

1

Step-by-step explanation:

3 0
3 years ago
What is the slope of a line that passes through the points (1, -2) and (-3,-6)?
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positive slope

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3 years ago
Read 2 more answers
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