Graph a quadratic by completing the square by factoring out a negative 1

The video tutorial explains how to graph a quadratic equation by completing the square. It begins with converting the quadratic from standard form to vertex form. The process involves factoring out a negative, completing the square, and determining the vertex. The tutorial also covers how to graph the quadratic, noting the direction of the parabola and its vertex. The video concludes with a demonstration of plotting the graph and understanding its properties.

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

• Divide by the coefficient of x

• Add a constant to both sides

• Factor out the negative sign

• Multiply by a constant

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

• Divide it by 2 and square it

• Subtract it from the quadratic term

• Add it to the constant term

• Multiply it by 2

Why is it necessary to subtract the square of half the linear coefficient after adding it inside the parentheses?

• To change the direction of the graph

• To simplify the equation

• To eliminate the constant term

• To maintain the balance of the equation

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

• (8, 20)

• (4, 36)

• (0, 0)

• (-4, -36)

How does the sign of 'a' in the quadratic equation affect the graph?

• It affects the color of the graph

• It determines the width of the graph

• It indicates whether the graph opens up or down

• It changes the vertex position