Finding the Minimum Value of a Quadratic Function by Completing the Square

This video tutorial teaches how to rewrite quadratic functions to reveal their minimum values by completing the square. It covers graphing quadratic functions, identifying minimum points, and provides a step-by-step example of completing the square. Common mistakes are discussed, and the process of finding minimum values using the completed square form is demonstrated.

What is the purpose of rewriting a quadratic function by completing the square?

• To eliminate the quadratic term

• To change the function into a linear equation

• To reveal the minimum value of the function

• To find the maximum value of the function

Which of the following is a common mistake when completing the square?

• Ignoring the constant term

• Forgetting to add and subtract the same number

• Multiplying the quadratic term by a constant

• Changing the sign of the linear term

In the expression (X + a)^2, what does 'a' represent?

• The coefficient of the quadratic term

• Half of the linear coefficient

• The constant term

• The minimum value of the function

What is the minimum value of the function y = X^2 - 12X + 49?

• 49

• 0

• 13

• 6

When completing the square for y = X^2 - 12X + 49, what value of X makes the square term zero?

• 49

• 6

• 0

• 12

How does rewriting a quadratic function help in understanding its graph?

• It changes the graph to a linear form

• It reveals the minimum point clearly

• It makes the maximum point more visible

• It eliminates the need for graphing

What is the smallest number you can add to 13 to get the minimum value of the function?

• 1

• 0

• 6

• 12