# Graph ( square root of x+4+x^2)(12) (x+4+x2)(12)
Reorder 12x+4 and 12×2.
y=12×2+12x+4
Find the domain for y=(x+4+x2)(12) so that a list of x values can be picked to find a list of points, which will help graphing the radical.
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}
To find the radical expression end point, substitute the x value -4, which is the least value in the domain, into f(x)=12×2+12x+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)
Select a few x values from the domain. It would be more useful to select the values so that they are next to the x value of the radical expression end point.
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)   ## Download our App from the store

### Create a High Performed UI/UX Design from a Silicon Valley.  Scroll to top