Question

Write a polynomial that could be represented by the graph.
(Which one is correct and why)

Answer 1

C

Explanation:

the graph has 3 zero solutions (values of x with y = 0).

therefore it has to be of 3rd degree (3 is the max. exponent of x).

that eliminates B, because it is only of 2nd degree.

when x = 0, y is a little bit below -60 but above -80.

but y is negative.

that eliminates A, because when x = 0, y = +64.

for x = -8, y has to be 0 too.

that eliminates D, because for x = -8, y = -8³ - 64 = -512 - 64 = -576

and not 0.

so, C must be correct.

for x = 0, y = -64

for x = -8, y = -8³ + 6×-8² - 24×-8 - 64 =

= -512 + 6×64 + 192 - 64 =

= -512 + 384 + 192 - 64 = 0

for x = -2, y = -2³ + 6×-2² - 24×-2 - 64 =

= -8 + 6×4 + 48 - 64 =

= -8 + 24 + 48 - 64 = 0

for x = 4, y = 4³ + 6×4² - 24×4 - 64 =

= 64 + 6×16 - 96 - 64 =

= 64 + 96 - 96 - 64 = 0

all fits.

Answer 2

your answer is C

Explanation:

by elimination B is not possible as the graph shows a cubic shape B has no cubic terms, D is not possible because the graph shows a translation on X axis and D represents a translation in Y axis, and A is not possible because when X=0 the value of Y must be -64 and A doesn't comply to that.