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What polynomial has a graph that passes through the given points? (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329) a)y = 2x3 – 3x2 – 2x + 1 b)y = 1x4 – 2x3 – 3x2 + 2x + 1 c)y = x4 – 2x3 + 3x2 + 2x – 1. d)y = x4 + 2x3 – 3x2 – 2x + 1

Verified Answer :

meerkat18

The way to answer this problem given different points and different equations in the choices is to do substitution and trial and error. In this regard, we substitute for example 4 to x in the equations and check which of them yields 89. The answer is D.

calculista

Let

\(A (-4, 89) B (-3, 7)C (-1, -1) D (1, -1)E (4, 329)\)

Using a graph tool

case a) \(y = 2x^{3}-3x^{2}-2x + 1\)

see the attached figure N \(1\)

The polynomial is not the solution

case b) \(y = x^{4}-2x^{3}-3x^{2} + 2x+1\)

see the attached figure N \(2\)

The polynomial is not the solution

case c) \(y = x^{4}-2x^{3}+3x^{2} + 2x-1\)

see the attached figure N \(3\)

The polynomial is not the solution

case d) \(y = x^{4}+2x^{3}-3x^{2} - 2x+1\)

see the attached figure N \(4\)

The polynomial pass through all the points

therefore

the answer is the polynomial

d) \(y = x^{4}+2x^{3}-3x^{2} - 2x+1\)

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