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Dahasolnce [82]
3 years ago
14

The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).

Mathematics
1 answer:
kow [346]3 years ago
6 0

Answer:

I(x) = 12x² + 8x + 5

Step-by-step explanation:

* Lets talk about the solution

- P(x) is a quadratic function represented graphically by a parabola

- The general form of the quadratic function is f(x) = ax² + bx + c,

  where a is the coefficient of x² and b is the coefficient of x and c is

  the y-intercept

- To find I(x) from P(x) change each x in P by 2x

∵ P(x) is dilated to I(x) by change x by 2x

∵ I(x) = P(2x)

∵ P(x) = 3x² + 4x + 5

∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify

∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²

∵ 4(2x) = 8x

∴ I(x) = 3(4x²) + 8x + 5

∵ 3(4x²) = 12x²

∴ I(x) = 12x² + 8x + 5

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valentinak56 [21]

The area of the shaded region is 3x^2 + 6x

<h3>How to determine the area of the shaded region?</h3>

The given parameters are:

  • Top side of the shaded rectangle = 2x + 7.
  • Left side of the shaded rectangle = 2x.
  • Top side of the unshaded rectangle = x + 8.
  • Left side of the unshaded rectangle = x.

The area of the shaded region is calculated as:

Shaded region area = (Top side of the shaded rectangle * Left side of the shaded rectangle) - (Top side of the unshaded rectangle * Left side of the unshaded rectangle)

Substitute the known values in the above equation

Shaded region area = (2x + 7) * (2x) - (x + 8) * (x)

Evaluate the products

Shaded region area = (4x^2 + 14x) - (x^2 + 8x)

Open the bracket

Shaded region area = 4x^2 + 14x - x^2 - 8x

Collect the like terms

Shaded region area = 4x^2 - x^2 + 14x  - 8x

Evaluate the like terms

Shaded region area = 3x^2 + 6x

Hence, the area of the shaded region is 3x^2 + 6x

Read more about areas at:

brainly.com/question/25292087

#SPJ1

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