(x+4+x2)(12)

Reorder 12x+4 and 12×2.

y=12×2+12x+4

Set the radicand in x+4 greater than or equal to 0 to find where the expression is defined.

x+4≥0

Subtract 4 from both sides of the inequality.

x≥-4

The domain is all values of x that make the expression defined.

Interval Notation:

[-4,∞)

Set-Builder Notation:

{x|x≥-4}

Interval Notation:

[-4,∞)

Set-Builder Notation:

{x|x≥-4}

Replace the variable x with -4 in the expression.

f(-4)=12(-4)2+12(-4)+4

Simplify the result.

Simplify each term.

Raise -4 to the power of 2.

f(-4)=12⋅16+12(-4)+4

Multiply 12 by 16.

f(-4)=192+12(-4)+4

Add -4 and 4.

f(-4)=192+120

Rewrite 0 as 02.

f(-4)=192+1202

Pull terms out from under the radical, assuming positive real numbers.

f(-4)=192+12⋅0

Multiply 12 by 0.

f(-4)=192+0

f(-4)=192+0

Add 192 and 0.

f(-4)=192

The final answer is 192.

192

192

192

The radical expression end point is (-4,192).

(-4,192)

Substitute the x value -3 into f(x)=12×2+12x+4. In this case, the point is (-3,120).

Replace the variable x with -3 in the expression.

f(-3)=12(-3)2+12(-3)+4

Simplify the result.

Simplify each term.

Raise -3 to the power of 2.

f(-3)=12⋅9+12(-3)+4

Multiply 12 by 9.

f(-3)=108+12(-3)+4

Add -3 and 4.

f(-3)=108+121

Any root of 1 is 1.

f(-3)=108+12⋅1

Multiply 12 by 1.

f(-3)=108+12

f(-3)=108+12

Add 108 and 12.

f(-3)=120

The final answer is 120.

y=120

y=120

y=120

Substitute the x value -2 into f(x)=12×2+12x+4. In this case, the point is (-2,48+122).

Replace the variable x with -2 in the expression.

f(-2)=12(-2)2+12(-2)+4

Simplify the result.

Simplify each term.

Raise -2 to the power of 2.

f(-2)=12⋅4+12(-2)+4

Multiply 12 by 4.

f(-2)=48+12(-2)+4

Add -2 and 4.

f(-2)=48+122

f(-2)=48+122

The final answer is 48+122.

y=48+122

y=48+122

y=48+122

The square root can be graphed using the points around the vertex (-4,192),(-3,120),(-2,64.97)

xy-4192-3120-264.97

xy-4192-3120-264.97

Graph ( square root of x+4+x^2)(12)