Graph t(x)=x^3+3x^2-36x-108

Math
t(x)=x3+3×2-36x-108
Find the point at x=-3.
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Replace the variable x with -3 in the expression.
f(-3)=(-3)3+3(-3)2-36⋅-3-108
Simplify the result.
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Simplify each term.
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Raise -3 to the power of 3.
f(-3)=-27+3(-3)2-36⋅-3-108
Raise -3 to the power of 2.
f(-3)=-27+3⋅9-36⋅-3-108
Multiply 3 by 9.
f(-3)=-27+27-36⋅-3-108
Multiply -36 by -3.
f(-3)=-27+27+108-108
f(-3)=-27+27+108-108
Simplify by adding and subtracting.
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Add -27 and 27.
f(-3)=0+108-108
Add 0 and 108.
f(-3)=108-108
Subtract 108 from 108.
f(-3)=0
f(-3)=0
The final answer is 0.
0
0
Convert 0 to decimal.
y=0
y=0
Find the point at x=-2.
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Replace the variable x with -2 in the expression.
f(-2)=(-2)3+3(-2)2-36⋅-2-108
Simplify the result.
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Simplify each term.
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Raise -2 to the power of 3.
f(-2)=-8+3(-2)2-36⋅-2-108
Raise -2 to the power of 2.
f(-2)=-8+3⋅4-36⋅-2-108
Multiply 3 by 4.
f(-2)=-8+12-36⋅-2-108
Multiply -36 by -2.
f(-2)=-8+12+72-108
f(-2)=-8+12+72-108
Simplify by adding and subtracting.
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Add -8 and 12.
f(-2)=4+72-108
Add 4 and 72.
f(-2)=76-108
Subtract 108 from 76.
f(-2)=-32
f(-2)=-32
The final answer is -32.
-32
-32
Convert -32 to decimal.
y=-32
y=-32
Find the point at x=-1.
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Replace the variable x with -1 in the expression.
f(-1)=(-1)3+3(-1)2-36⋅-1-108
Simplify the result.
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Simplify each term.
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Raise -1 to the power of 3.
f(-1)=-1+3(-1)2-36⋅-1-108
Raise -1 to the power of 2.
f(-1)=-1+3⋅1-36⋅-1-108
Multiply 3 by 1.
f(-1)=-1+3-36⋅-1-108
Multiply -36 by -1.
f(-1)=-1+3+36-108
f(-1)=-1+3+36-108
Simplify by adding and subtracting.
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Add -1 and 3.
f(-1)=2+36-108
Add 2 and 36.
f(-1)=38-108
Subtract 108 from 38.
f(-1)=-70
f(-1)=-70
The final answer is -70.
-70
-70
Convert -70 to decimal.
y=-70
y=-70
Find the point at x=0.
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Replace the variable x with 0 in the expression.
f(0)=(0)3+3(0)2-36⋅0-108
Simplify the result.
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Simplify each term.
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Raising 0 to any positive power yields 0.
f(0)=0+3(0)2-36⋅0-108
Raising 0 to any positive power yields 0.
f(0)=0+3⋅0-36⋅0-108
Multiply 3 by 0.
f(0)=0+0-36⋅0-108
Multiply -36 by 0.
f(0)=0+0+0-108
f(0)=0+0+0-108
Simplify by adding zeros.
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Add 0 and 0.
f(0)=0+0-108
Add 0 and 0.
f(0)=0-108
Subtract 108 from 0.
f(0)=-108
f(0)=-108
The final answer is -108.
-108
-108
Convert -108 to decimal.
y=-108
y=-108
Find the point at x=1.
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Replace the variable x with 1 in the expression.
f(1)=(1)3+3(1)2-36⋅1-108
Simplify the result.
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Simplify each term.
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One to any power is one.
f(1)=1+3(1)2-36⋅1-108
One to any power is one.
f(1)=1+3⋅1-36⋅1-108
Multiply 3 by 1.
f(1)=1+3-36⋅1-108
Multiply -36 by 1.
f(1)=1+3-36-108
f(1)=1+3-36-108
Simplify by adding and subtracting.
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Add 1 and 3.
f(1)=4-36-108
Subtract 36 from 4.
f(1)=-32-108
Subtract 108 from -32.
f(1)=-140
f(1)=-140
The final answer is -140.
-140
-140
Convert -140 to decimal.
y=-140
y=-140
The cubic function can be graphed using the function behavior and the points.
xy-30-2-32-1-700-1081-140
The cubic function can be graphed using the function behavior and the selected points.
Falls to the left and rises to the right
xy-30-2-32-1-700-1081-140
Graph t(x)=x^3+3x^2-36x-108

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