Use the key features of the polynomial f(x) = -4x^4 + 4x^3 + 9x^2 – 12x + 10 to describe its end behavior.

The left side continues up, and the right side continues up.

The left side continues down, and the right side continues down

The left side continues up, and the right side continues down

The left side continues down, and the right side continues up

The left side continues down, and the right side continues down

Step-by-step explanation:

f(x) = -4x⁴ + 4x³ + 9x² – 12x + 10

The leading term (-4x⁴) has an even exponent and a negative coefficient.

Since the exponent is even, the left and right ends will continue in the same direction.

Since the coefficient is negative, both ends will continue down.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true