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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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