Completing the square by creating a fraction to graph a quadratic in vertex form

This video tutorial explains how to graph a quadratic equation by converting it from standard form to vertex form using the method of completing the square. It covers the process of creating a perfect square trinomial, factoring it into a binomial squared, and then graphing the resulting quadratic function. The tutorial also discusses how to determine the vertex and the direction in which the graph opens, providing a step-by-step guide to plotting the function on a graph.

What is the first step in converting a quadratic equation from standard form to vertex form?

• Divide the equation by the constant term

• Ensure the leading coefficient is zero

• Ensure the leading coefficient is one

• Multiply the equation by two

What is the standard form of a quadratic equation?

• y = a(x + b)^2 + c

• y = ax + b

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

When completing the square, what value do you calculate and add to both sides of the equation?

• 2b

• (b/2)^2

• b/2

• b^2

Why is creating a perfect square trinomial useful in the process of completing the square?

• It makes the equation longer

• It simplifies factoring into a binomial squared

• It changes the direction of the parabola

• It eliminates the need for a constant term

What is the vertex of the quadratic function after completing the square?

• (5, 33)

• (-2.5, -8.25)

• (-5, -33)

• (2.5, 8.25)

How do you determine the direction in which the parabola opens?

• By checking the value of b

• By checking the value of the vertex

• By checking the sign of the leading coefficient

• By checking the sign of the constant term

What is the significance of the vertex in graphing a quadratic function?

• It eliminates the need for graphing

• It determines the width of the parabola

• It changes the equation to standard form

• It is the highest or lowest point on the graph