If p(𝑥) = 𝑥2 - 4𝑥 + 3, evaluate: 𝑝(2)− 𝑝(−1) + 𝑝(1/2).

Given 

p( ) = 2 – 4  + 3

According to the given details

When x = 2,

p(x) = p(2)

p( ) = 2 – 4  + 3

Substituting x = 2,

p(2) = (2)2 – 4(2) + 3

= 4 – 8 + 3

= – 4 + 3

= – 1

When x = – 1,

p(x) = p(– 1)

p( ) = 2 – 4  + 3

Substituting x = – 1,

p(– 1) = (– 1)2 – 4(– 1) + 3

= 1 + 4 + 3

= 8

When x = 1/2 ,

p(x) = p(1/2)

p( ) = 2 – 4  + 3

Substituting x = 1/2,

p(1/2) = (1/2)2 – 4(1/2) + 3

= ¼ – 2 + 3

= ¼ + 1

= 5/4

Now,

p(2)− p(−1) + p(1/2) = – 1 – 8 + (5/4)

= – 9 + (5/4)

= ( – 36 + 5)/4

= – 31/4

Answer

p(2)− p(−1) + p(1/2) =-31/4

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