In Exercises 33–38, express the function, f, in simplified form. ...

Question

In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number.
___________
f(x) = √5x² - 10x + 5

Accepted Answer

Completely simplify the following function note that any variable that appears represents positive numbers where our function is the square root of seven U squared Plus 28 U plus 28. Now, one thing we can do first is factor out the seven to simplify this a little bit better. We look at the square root of seven multiplied by U squared Plus four U Plus four. Now we are allowed to separate our radical and separate this as a square root of seven multiplied by the square root of U squared plus four U plus four. Now we can work on the radical to the right here, take the square root view squared, we can separate our four U into two U plus two U And bring down our 4th. Now we can factor by grouping together terms in our first two terms, we have U squared into U, we can factor out and you giving us U multiplied by U plus two. On our second set of terms, we can factor the two to get two multiplied by U plus two. We notice we have U plus two appearing twice. We can then rewrite this as U plus two multiplied by U plus two, combining everything that's remaining outside of the parentheses. We notice we have two copies of U plus two. The squared of U plus two twice will be just U plus two by itself. We can then write this as a square of seven multiplied by U plus two, rearranging. We get U plus two first multiplied by the square root of seven. We can't simplify this anymore. So we determine the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. ___________ f(x) = √5x² - 10x + 5

Key Concepts

Quadratic Functions

Completing the Square

Square Roots and Simplification

Watch next