Trigonometry Examples

Find the Maximum/Minimum Value f(x)=(x+7)^2-1
Step 1
Simplify each term.
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Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Move to the left of .
Step 1.3.1.3
Multiply by .
Step 1.3.2
Add and .
Step 2
Subtract from .
Step 3
The minimum of a quadratic function occurs at . If is positive, the minimum value of the function is .
occurs at
Step 4
Find the value of .
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Step 4.1
Substitute in the values of and .
Step 4.2
Remove parentheses.
Step 4.3
Simplify .
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Step 4.3.1
Cancel the common factor of and .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Cancel the common factors.
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Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Cancel the common factor.
Step 4.3.1.2.3
Rewrite the expression.
Step 4.3.1.2.4
Divide by .
Step 4.3.2
Multiply by .
Step 5
Evaluate .
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Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
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Step 5.2.1
Simplify each term.
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Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Multiply by .
Step 5.2.2
Simplify by adding and subtracting.
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Step 5.2.2.1
Subtract from .
Step 5.2.2.2
Add and .
Step 5.2.3
The final answer is .
Step 6
Use the and values to find where the minimum occurs.
Step 7