Finding Maximum and Minimum Turning Points using Completing the Square

The video tutorial covers the concept of completing the square, a method used to solve quadratic equations and find maximum and minimum points on graphs. It explains the process of transforming a quadratic equation into its completed square form and demonstrates how this form can be used to identify turning points and solve equations. The tutorial includes several example problems, illustrating both basic and advanced applications of the method. Key concepts such as graph transformations and the distinction between positive and negative quadratics are also discussed.

What is one of the main uses of completing the square in quadratic equations?

• To determine the maximum and minimum points on a graph

• To calculate the area under a curve

• To find the roots of linear equations

• To solve cubic equations

When completing the square, what do you do with the coefficient of the linear term?

• Halve it

• Square it

• Ignore it

• Double it

How does a positive quadratic equation affect the turning point?

• It creates a maximum turning point

• It creates a minimum turning point

• It has no effect on the turning point

• It creates both maximum and minimum turning points

In the completed square form y = (x + p)^2 + q, what does the value of 'p' represent?

• The y-intercept of the graph

• The vertical shift of the graph

• The horizontal shift of the graph

• The slope of the graph

What is the effect of adding a constant to the x-value in a quadratic equation?

• Reflects the graph over the x-axis

• Shifts the graph vertically

• Shifts the graph horizontally

• Changes the slope of the graph

What is the turning point of the quadratic equation y = (x + 3)^2 - 4?

• (-3, 4)

• (3, -4)

• (-3, -4)

• (3, 4)

In the equation y = (x + 1)^2 - 10, what is the turning point?

• (1, -10)

• (-1, -10)

• (1, 10)

• (-1, 10)

How do you find the roots of a quadratic equation in completed square form?

• By graphing the equation

• By setting the equation to zero and solving

• By using the quadratic formula

• By expanding and simplifying

What is the shape of the graph for a negative quadratic equation?

• U-shaped

• W-shaped

• N-shaped

• V-shaped

What is the turning point of the equation y = -2(x - 3/4)^2 + 65/8?

• (-3/4, -65/8)

• (3/4, -65/8)

• (-3/4, 65/8)

• (3/4, 65/8)