The function p(x) = 3x2 + 4x + 5,is dilated by the function i(x) = p(2x). write the new function i(x).

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

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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