# Graph y=2x^4-20x^3+32x^2

y=2×4-20×3+32×2
Find the point at x=0.
Replace the variable x with 0 in the expression.
f(0)=2(0)4-20(0)3+32(0)2
Simplify the result.
Simplify each term.
Raising 0 to any positive power yields 0.
f(0)=2⋅0-20(0)3+32(0)2
Multiply 2 by 0.
f(0)=0-20(0)3+32(0)2
Raising 0 to any positive power yields 0.
f(0)=0-20⋅0+32(0)2
Multiply -20 by 0.
f(0)=0+0+32(0)2
Raising 0 to any positive power yields 0.
f(0)=0+0+32⋅0
Multiply 32 by 0.
f(0)=0+0+0
f(0)=0+0+0
f(0)=0+0
f(0)=0
f(0)=0
0
0
Convert 0 to decimal.
y=0
y=0
Find the point at x=1.
Replace the variable x with 1 in the expression.
f(1)=2(1)4-20(1)3+32(1)2
Simplify the result.
Simplify each term.
One to any power is one.
f(1)=2⋅1-20(1)3+32(1)2
Multiply 2 by 1.
f(1)=2-20(1)3+32(1)2
One to any power is one.
f(1)=2-20⋅1+32(1)2
Multiply -20 by 1.
f(1)=2-20+32(1)2
One to any power is one.
f(1)=2-20+32⋅1
Multiply 32 by 1.
f(1)=2-20+32
f(1)=2-20+32
Subtract 20 from 2.
f(1)=-18+32
f(1)=14
f(1)=14
14
14
Convert 14 to decimal.
y=14
y=14
Find the point at x=2.
Replace the variable x with 2 in the expression.
f(2)=2(2)4-20(2)3+32(2)2
Simplify the result.
Simplify each term.
Multiply 2 by (2)4 by adding the exponents.
Multiply 2 by (2)4.
Raise 2 to the power of 1.
f(2)=2(2)4-20(2)3+32(2)2
Use the power rule aman=am+n to combine exponents.
f(2)=21+4-20(2)3+32(2)2
f(2)=21+4-20(2)3+32(2)2
f(2)=25-20(2)3+32(2)2
f(2)=25-20(2)3+32(2)2
Raise 2 to the power of 5.
f(2)=32-20(2)3+32(2)2
Raise 2 to the power of 3.
f(2)=32-20⋅8+32(2)2
Multiply -20 by 8.
f(2)=32-160+32(2)2
Raise 2 to the power of 2.
f(2)=32-160+32⋅4
Multiply 32 by 4.
f(2)=32-160+128
f(2)=32-160+128
Subtract 160 from 32.
f(2)=-128+128
f(2)=0
f(2)=0
0
0
Convert 0 to decimal.
y=0
y=0
Find the point at x=3.
Replace the variable x with 3 in the expression.
f(3)=2(3)4-20(3)3+32(3)2
Simplify the result.
Simplify each term.
Raise 3 to the power of 4.
f(3)=2⋅81-20(3)3+32(3)2
Multiply 2 by 81.
f(3)=162-20(3)3+32(3)2
Raise 3 to the power of 3.
f(3)=162-20⋅27+32(3)2
Multiply -20 by 27.
f(3)=162-540+32(3)2
Raise 3 to the power of 2.
f(3)=162-540+32⋅9
Multiply 32 by 9.
f(3)=162-540+288
f(3)=162-540+288
Subtract 540 from 162.
f(3)=-378+288
f(3)=-90
f(3)=-90
-90
-90
Convert -90 to decimal.
y=-90
y=-90
Find the point at x=4.
Replace the variable x with 4 in the expression.
f(4)=2(4)4-20(4)3+32(4)2
Simplify the result.
Simplify each term.
Raise 4 to the power of 4.
f(4)=2⋅256-20(4)3+32(4)2
Multiply 2 by 256.
f(4)=512-20(4)3+32(4)2
Raise 4 to the power of 3.
f(4)=512-20⋅64+32(4)2
Multiply -20 by 64.
f(4)=512-1280+32(4)2
Raise 4 to the power of 2.
f(4)=512-1280+32⋅16
Multiply 32 by 16.
f(4)=512-1280+512
f(4)=512-1280+512
Subtract 1280 from 512.
f(4)=-768+512
f(4)=-256
f(4)=-256
-256
-256
Convert -256 to decimal.
y=-256
y=-256
The 4th degree function can be graphed using the function behavior and the points.
xy00114203-904-256
The 4th degree function can be graphed using the function behavior and the selected points.
Rises to the left and rises to the right
xy00114203-904-256
Graph y=2x^4-20x^3+32x^2