Graphing the parabola by completing the square and find the focus and directrix

The video tutorial covers solving quadratic equations by completing the square, creating perfect square trinomials, and identifying the vertex and focus of a parabola. It also explains how to graph the parabola and understand its properties, such as the directrix and the direction it opens.

What is the first step in rearranging an equation to isolate variables?

• Add constants to both sides

• Multiply both sides by a constant

• Get all variables on one side

• Divide both sides by a variable

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

• Subtract it from the quadratic term

• Add it to the constant term

• Divide it by 2 and square it

• Multiply it by 2

What is the result of completing the square on a quadratic expression?

• A perfect square trinomial

• A constant term

• A linear equation

• A quadratic equation

Why is it important to factor out the coefficient when formatting equations?

• To make the equation linear

• To simplify the equation

• To ensure the equation is in the correct format

• To eliminate the constant term

What is the vertex of a parabola in the form (x - h)^2 = 4p(y - k)?

• (k, h)

• (-h, -k)

• (h, k)

• (-k, -h)

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

• By the sign of the coefficient of x

• By the sign of the coefficient of y

• By the distance from the vertex to the focus

• By the value of the directrix

What is the relationship between the vertex and the directrix of a parabola?

• The vertex is always to the left of the directrix

• The vertex is always below the directrix

• The vertex is equidistant from the focus and the directrix

• The vertex is always above the directrix