Describing key features of a graph of a polynomial function: explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.

End behavior:

The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.

Zeroes:

f(x) = x³ + 2x² - 8x

0 = x³ + 2x² - 8x

0 = x(x² + 2x - 8)    

0 = x(x + 4)(x - 2)

0 = x         0 = x + 4         0 = x - 2

x = 0            x = -4              x = 2

Intervals:

Put the zeroes in order: -4, 0, 2

since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.

Graph:

see attachment

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it