p(x)=3×3+6×2-4x-3

Replace the variable x with -2 in the expression.

f(-2)=3(-2)3+6(-2)2-4⋅-2-3

Simplify the result.

Simplify each term.

Raise -2 to the power of 3.

f(-2)=3⋅-8+6(-2)2-4⋅-2-3

Multiply 3 by -8.

f(-2)=-24+6(-2)2-4⋅-2-3

Raise -2 to the power of 2.

f(-2)=-24+6⋅4-4⋅-2-3

Multiply 6 by 4.

f(-2)=-24+24-4⋅-2-3

Multiply -4 by -2.

f(-2)=-24+24+8-3

f(-2)=-24+24+8-3

Simplify by adding and subtracting.

Add -24 and 24.

f(-2)=0+8-3

Add 0 and 8.

f(-2)=8-3

Subtract 3 from 8.

f(-2)=5

f(-2)=5

The final answer is 5.

5

5

Convert 5 to decimal.

y=5

y=5

Replace the variable x with -1 in the expression.

f(-1)=3(-1)3+6(-1)2-4⋅-1-3

Simplify the result.

Simplify each term.

Raise -1 to the power of 3.

f(-1)=3⋅-1+6(-1)2-4⋅-1-3

Multiply 3 by -1.

f(-1)=-3+6(-1)2-4⋅-1-3

Raise -1 to the power of 2.

f(-1)=-3+6⋅1-4⋅-1-3

Multiply 6 by 1.

f(-1)=-3+6-4⋅-1-3

Multiply -4 by -1.

f(-1)=-3+6+4-3

f(-1)=-3+6+4-3

Simplify by adding and subtracting.

Add -3 and 6.

f(-1)=3+4-3

Add 3 and 4.

f(-1)=7-3

Subtract 3 from 7.

f(-1)=4

f(-1)=4

The final answer is 4.

4

4

Convert 4 to decimal.

y=4

y=4

Replace the variable x with 0 in the expression.

f(0)=3(0)3+6(0)2-4⋅0-3

Simplify the result.

Simplify each term.

Raising 0 to any positive power yields 0.

f(0)=3⋅0+6(0)2-4⋅0-3

Multiply 3 by 0.

f(0)=0+6(0)2-4⋅0-3

Raising 0 to any positive power yields 0.

f(0)=0+6⋅0-4⋅0-3

Multiply 6 by 0.

f(0)=0+0-4⋅0-3

Multiply -4 by 0.

f(0)=0+0+0-3

f(0)=0+0+0-3

Simplify by adding zeros.

Add 0 and 0.

f(0)=0+0-3

Add 0 and 0.

f(0)=0-3

Subtract 3 from 0.

f(0)=-3

f(0)=-3

The final answer is -3.

-3

-3

Convert -3 to decimal.

y=-3

y=-3

Replace the variable x with 1 in the expression.

f(1)=3(1)3+6(1)2-4⋅1-3

Simplify the result.

Simplify each term.

One to any power is one.

f(1)=3⋅1+6(1)2-4⋅1-3

Multiply 3 by 1.

f(1)=3+6(1)2-4⋅1-3

One to any power is one.

f(1)=3+6⋅1-4⋅1-3

Multiply 6 by 1.

f(1)=3+6-4⋅1-3

Multiply -4 by 1.

f(1)=3+6-4-3

f(1)=3+6-4-3

Simplify by adding and subtracting.

Add 3 and 6.

f(1)=9-4-3

Subtract 4 from 9.

f(1)=5-3

Subtract 3 from 5.

f(1)=2

f(1)=2

The final answer is 2.

2

2

Convert 2 to decimal.

y=2

y=2

Replace the variable x with 2 in the expression.

f(2)=3(2)3+6(2)2-4⋅2-3

Simplify the result.

Simplify each term.

Raise 2 to the power of 3.

f(2)=3⋅8+6(2)2-4⋅2-3

Multiply 3 by 8.

f(2)=24+6(2)2-4⋅2-3

Raise 2 to the power of 2.

f(2)=24+6⋅4-4⋅2-3

Multiply 6 by 4.

f(2)=24+24-4⋅2-3

Multiply -4 by 2.

f(2)=24+24-8-3

f(2)=24+24-8-3

Simplify by adding and subtracting.

Add 24 and 24.

f(2)=48-8-3

Subtract 8 from 48.

f(2)=40-3

Subtract 3 from 40.

f(2)=37

f(2)=37

The final answer is 37.

37

37

Convert 37 to decimal.

y=37

y=37

The cubic function can be graphed using the function behavior and the points.

xy-25-140-312237

The cubic function can be graphed using the function behavior and the selected points.

Falls to the left and rises to the right

xy-25-140-312237

Graph p(x)=3x^3+6x^2-4x-3