Question

Algebra 2 please help

Answer 1

Answer:

Here's what I get  

Step-by-step explanation:

a) Possible degree

This  looks like the graph of a cubic equation.

ƒ(x) could be a third degree function.

b) Sign of leading coefficient

As x ⟶ ∞, ƒ(x) ⟶ ∞.

The leading coefficient must be positive.

c) Coordinates of maxima and minima

There is a local maximum at (-4, 0) and a local minimum at about (-1, -18.).

d) Coordinates of zeros

There are zeros at (-4, 0) and (1, 0).

e) Increasing and decreasing intervals

ƒ(x) is increasing in the intervals (-∞, -4) and (-1, ∞).

ƒ(x) is decreasing in the interval (-4, -1).

f) Negative intervals

The graph is negative in the intervals (-∞, -4) and (-4, ∞).

g) Possible factored form of equation

A cubic equation must have three roots. This function has a root at x = 1. Another is at x = -4. That root just touches the x-axis, so it must be degenerate (occur twice).

The factored form of the equation is

ƒ(x) = (x - 1)(x + 4)(x + 4)

h) End behaviour

ƒ(x) ⟶ -∞ as x ⟶ -∞ and ƒ(x) ⟶ ∞ as x ⟶ ∞ .