Question

Which of the given polynomial function passes through the points (2,5), (3,2) and (4,5)?

Select one:
p(x)=19-18x+3x^{2}
p(x)=19-18x+4x^{2}
p(x)=29-18x+4x^{2}
p(x)=29-18x+3x^{2}

Answer 1

Answer:

The fourth one:  p(x) = 29 - 18x + 3x²

Step-by-step explanation:

Try first polynomial p(x) = 19 - 18x + 3x²

Does it pass through (2,5)?  p(2) = 19 - 36 + 12 ≠ 5.  No it does not.

Try second polynomial p(x) = 19 - 18x + 4x²

Does it pass through (2,5)?  p(2) = 19 - 36 + 16 ≠ 5.  No it does not.

Try third polynomial p(x) = 29 - 18x + 4x²

Does it pass through (2,5)?  p(2) = 29 - 36 + 16 ≠ 5.  No it does not.

The answer must be the fourth polynomial.

But let's check anyway.

Try fourth polynomial p(x) = 29 - 18x + 3x²

Does it pass through (2,5)?  p(2) = 29 - 36 + 12 = 5.  Yes it does.

Does it pass through (3,2)?  p(3) = 29 - 54 + 27 = 2.  Yes it does.

Does it pass through (4,5)?  p(4) = 29 - 72 + 48 = 5.  Yes it does.

Confirmed... This polynomial pass through all 3 of the given points.