y=2×4-20×3+32×2

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

Simplify by adding zeros.

Add 0 and 0.

f(0)=0+0

Add 0 and 0.

f(0)=0

f(0)=0

The final answer is 0.

0

0

Convert 0 to decimal.

y=0

y=0

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

Simplify by adding and subtracting.

Subtract 20 from 2.

f(1)=-18+32

Add -18 and 32.

f(1)=14

f(1)=14

The final answer is 14.

14

14

Convert 14 to decimal.

y=14

y=14

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

Add 1 and 4.

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

Simplify by adding and subtracting.

Subtract 160 from 32.

f(2)=-128+128

Add -128 and 128.

f(2)=0

f(2)=0

The final answer is 0.

0

0

Convert 0 to decimal.

y=0

y=0

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

Simplify by adding and subtracting.

Subtract 540 from 162.

f(3)=-378+288

Add -378 and 288.

f(3)=-90

f(3)=-90

The final answer is -90.

-90

-90

Convert -90 to decimal.

y=-90

y=-90

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

Simplify by adding and subtracting.

Subtract 1280 from 512.

f(4)=-768+512

Add -768 and 512.

f(4)=-256

f(4)=-256

The final answer is -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