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BigorU [14]
3 years ago
15

Create a polynomial function in factored form that crosses through the x-axis at -2 and touches the x-axis and turns around at 4

.​
Mathematics
1 answer:
UkoKoshka [18]3 years ago
3 0

Given:

A polynomial crosses through the x-axis at -2 and touches the x-axis and turns around at 4.​

To find:

The polynomial function in factored form.

Solution:

If the graph of a polynomial intersect the x-axis at x=a, then (x-a) is a factor of the polynomial.

If the graph of a polynomial touches the x-axis at x=b, then (x-b) is a factor of the polynomial with multiplicity 2. In other words (x-b)^2 is the factor of the polynomial.

It is given that the polynomial crosses through the x-axis at -2. So, (x+2) is a factor of required polynomial.

It is given that the polynomial touches the x-axis and turns around at 4. So, (x-4)^2 is a factor of required polynomial.

Now, the required polynomial is:

P(x)=(x+2)(x-4)^2

Therefore, the required polynomial is P(x)=(x+2)(x-4)^2.

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Answer:

Area of rectangle PQRS is 14 square units.

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Step-by-step explanation:

Let us find the area of each of the figures shown in the graph.

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From the graph,

Length of PQ = 7 units

Length of QS = 2 units

Now, area of rectangle PQRS = PQ\times QS=7\times 2=14 square units.

Now, area of square ABCD is given as the square of any of its side.

From the graph, AB = 4 units.

So, area of ABCD = AB^{2}=4^2=16 square units.

Area of triangle UVW is given as the half of the product of its base VW and height UW.

From the graph, UW = 4 units, VW = 8 units

Therefore, area of triangle UVW = \frac{1}{2}\times UW\times VW=\frac{1}{2}\times 4\times 8=16 square units.

For triangle EFG, EF = 4 units and FG = 8 units.

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Area of rectangle PQRS is 14 square units. The remaining figures have areas each equal to 16 square units.

4 0
3 years ago
Several ordered pairs from a continuous exponential function are shown in the table.
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Answer:

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Step-by-step explanation:

* Lets explain how to solve the problem

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* <em>The domain is {x : x ∈ R} , the range is {y : y > 0}</em>

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