Find the Range f(x)=2x-x^2-17

Locate the vertex of the parabola.
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Rewrite the equation in vertex form.
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Reorder and .
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 .
Simplify the right side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Add and .
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 negative, the parabola opens down.
Opens Down
Find the vertex .
The range of a parabola that opens down starts at its vertex and extends to negative infinity.
Interval Notation:
Set-Builder Notation:
Find the Range f(x)=2x-x^2-17

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