How to write an equation in vertex form and find the vertex

The video tutorial covers writing equations in standard form and sketching graphs. It begins with an introduction to the topic, followed by a detailed explanation of the completing the square method. An example problem is solved step-by-step, demonstrating how to find the perfect square and adjust the equation. Finally, the tutorial shows how to sketch the graph of the quadratic equation, identifying key features like the vertex and y-intercept.

What is the purpose of completing the square in a quadratic equation?

• To find the roots of the equation

• To convert the equation into a perfect square form

• To determine the y-intercept

• To calculate the slope of the graph

In the given quadratic problem, what is the value of 'b'?

• 10

• 8

• 4

• 1

How do you adjust the equation after adding a number to complete the square?

• Add the same number to both sides

• Subtract the same number from both sides

• Multiply the number by the coefficient of x

• Add and subtract the number on the same side

What does the vertex of the graph represent in the context of the quadratic equation?

• The point where the graph intersects the x-axis

• The highest point of the graph

• The point where the graph intersects the y-axis

• The turning point of the graph

If the coefficient 'a' in the quadratic equation is greater than one, what does it indicate about the graph?

• The graph is a circle

• The graph opens upwards

• The graph is a straight line

• The graph opens downwards