Trigonometry Examples

Find the Maximum/Minimum Value f(x)=-(x-5)^2+3
Step 1
Simplify each term.
Tap for more steps...
Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
Tap for more steps...
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.
Tap for more steps...
Step 1.3.1
Simplify each term.
Tap for more steps...
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
Subtract from .
Step 1.4
Apply the distributive property.
Step 1.5
Simplify.
Tap for more steps...
Step 1.5.1
Multiply by .
Step 1.5.2
Multiply by .
Step 2
Add and .
Step 3
The maximum of a quadratic function occurs at . If is negative, the maximum value of the function is .
occurs at
Step 4
Find the value of .
Tap for more steps...
Step 4.1
Substitute in the values of and .
Step 4.2
Remove parentheses.
Step 4.3
Simplify .
Tap for more steps...
Step 4.3.1
Cancel the common factor of and .
Tap for more steps...
Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Move the negative one from the denominator of .
Step 4.3.2
Multiply .
Tap for more steps...
Step 4.3.2.1
Multiply by .
Step 4.3.2.2
Multiply by .
Step 5
Evaluate .
Tap for more steps...
Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
Tap for more steps...
Step 5.2.1
Simplify each term.
Tap for more steps...
Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Multiply by .
Step 5.2.1.3
Multiply by .
Step 5.2.2
Simplify by adding and subtracting.
Tap for more steps...
Step 5.2.2.1
Add and .
Step 5.2.2.2
Subtract from .
Step 5.2.3
The final answer is .
Step 6
Use the and values to find where the maximum occurs.
Step 7