Finding Inverses of Quadratic Functions

This video tutorial explains how to find the inverse of a quadratic function. It begins by rewriting the function and then employs the method of completing the square to simplify the process. The tutorial guides through factoring the equation and finally finding the inverse by switching variables and solving for y. The video concludes with the final expression for the inverse function.

What is the initial form of the quadratic function given in the video?

• f(x) = 2x^2 - 6x - 2

• f(x) = 2x^2 - 6x + 2

• f(x) = 2x^2 + 6x + 2

• f(x) = 2x^2 + 6x - 2

What is the first step in finding the inverse of a quadratic function?

• Differentiate the function

• Switch x and y

• Complete the square

• Factor the quadratic

What is the purpose of completing the square in this context?

• To find the roots of the quadratic

• To rearrange the function for easier inversion

• To convert the quadratic into a linear function

• To simplify the function for easier differentiation

What value is added and subtracted to complete the square?

• 3

• 1

• 6

• 9

After completing the square, what is the new form of the quadratic function?

• y = 2(x + 3)^2 + 7

• y = 2(x + 3)^2 - 7

• y = 2(x - 3)^2 + 7

• y = 2(x - 3)^2 - 7

What is the next step after rearranging the quadratic function?

• Switch x and y

• Differentiate the function

• Solve for x

• Integrate the function

What equation do you get after switching x and y?

• x = 2(y + 3)^2 + 7

• x = 2(y - 3)^2 - 7

• x = 2(y + 3)^2 - 7

• x = 2(y - 3)^2 + 7

What operation is performed to isolate y in the equation x = 2(y - 3)^2 - 7?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 7 from both sides

• Add 7 to both sides

What is the result of taking the square root of both sides in the equation?

• y - 3 = ±√(x + 7)

• y + 3 = ±√(x + 7)

• y + 3 = ±√(x - 7)

• y - 3 = ±√(x - 7)

What is the final step to solve for y in the inverse function?

• Multiply both sides by 2

• Add 3 to both sides

• Subtract 3 from both sides

• Divide both sides by 2