Find the Range y=x^2+4x+6

Find the Range y=x^2+4x+6
Locate the vertex of the parabola.
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Rewrite the equation in vertex form.
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Complete the square for .
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Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
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Simplify each term.
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens up.
Opens Up
Find the vertex .
The range of a parabola that opens up starts at its vertex and extends to infinity.
Interval Notation:
Set-Builder Notation:
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