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3 years ago

Slide and transformation

Mathematics

1 answer:

Ludmilka [50]3 years ago

5 0

The rule that describes this transformation is (x - 3, y + 1)

Step-by-step explanation:

Step 1:

The points of the trapezoid are

M; (-3, -1),

N; (-4, 3),

P; (1, 3), and

Q; (-1, -1).

Step 2:

To translate the points to 3 units on the left, we subtract the x coordinate by 3 because it is moved to the left. So x becomes x - 3.

In order to translate the points to 1 unit up, we add 1 to the y coordinate as it is moved in the positive direction of y. So y becomes y + 1.

Combining these we get (x, y) becomes (x - 3, y + 1).

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OleMash [197]

Answer:

Part 1)

The possible multiplicities are:

$x=-7$ multiplicity 1

$x=-3$ multiplicity 3

$x=2$ multiplicity 1

$x=5$ multiplicity 2

Part 2

The factored form is

$p(x)=(x+7)(x+3)^3(x-2)(x-5)^2$

Step-by-step explanation:

Part 1.

The missing diagram is shown in the attachment.

The zeroes of the seventh degree polynomial are the x-intercepts of the graph.

From the graph, we have x-intercepts at:

$x=-7$ , $x=-3$ , $x=2$ , and $x=5$ .

The multiplicities tell us how many times a root repeats.

Also, even multiplicities will not cross their x-intercept, while odd multiplicities cross their x-intercepts.

The possible multiplicities are:

$x=-7$ multiplicity 1

$x=-3$ multiplicity 3

$x=2$ multiplicity 1

$x=5$ multiplicity 2

Note that the total multiplicity must equate the degree.

Part 2)

According to the factor theorem, if $x=a$ is a zero of p(x), then $(x-a)$ is a factor.

Using the multiplicities , we can write the factors as:

$x+7$

$(x+3)^3$

$(x-2)^1$

$(x-5)^2$

Therefore the completely factored form of this seventh degree polynomial is $p(x)=(x+7)(x+3)^3(x-2)(x-5)^2$

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If you're meaning write it in standard form it would be

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