# Graph p(x)=3x^3+6x^2-4x-3 p(x)=3×3+6×2-4x-3
Find the point at x=-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
f(-2)=0+8-3
f(-2)=8-3
Subtract 3 from 8.
f(-2)=5
f(-2)=5
5
5
Convert 5 to decimal.
y=5
y=5
Find the point at x=-1.
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
f(-1)=3+4-3
f(-1)=7-3
Subtract 3 from 7.
f(-1)=4
f(-1)=4
4
4
Convert 4 to decimal.
y=4
y=4
Find the point at x=0.
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
f(0)=0+0-3
f(0)=0-3
Subtract 3 from 0.
f(0)=-3
f(0)=-3
-3
-3
Convert -3 to decimal.
y=-3
y=-3
Find the point at x=1.
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
f(1)=9-4-3
Subtract 4 from 9.
f(1)=5-3
Subtract 3 from 5.
f(1)=2
f(1)=2
2
2
Convert 2 to decimal.
y=2
y=2
Find the point at x=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
f(2)=48-8-3
Subtract 8 from 48.
f(2)=40-3
Subtract 3 from 40.
f(2)=37
f(2)=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     