Completing the square to identify the vertex, focus and directrix of a parabola in conic

The video tutorial explains how to transform a quadratic equation into conics form, focusing on identifying the vertex, focus, and directrix. The instructor guides through completing the square, adjusting the equation to vertex form, and interpreting the graph. Key features of the conic section are identified, and the importance of proper equation formatting is emphasized.

What is the initial form of the equation given in the problem?

• X^2 + 20X + Y = -53

• 2X^2 + 20X + Y = 53

• X^2 + 20X - Y = 53

• 2X^2 + 20X - Y = -53

What is the first step in rearranging the equation to prepare for completing the square?

• Add 53 to both sides

• Factor out the coefficient of X^2

• Move Y to the other side

• Subtract 20X from both sides

Why do we factor out the coefficient of X^2 before completing the square?

• To make completing the square possible

• To ensure the equation is in standard form

• To make the equation linear

• To simplify the equation

What is the vertex of the parabola after completing the square?

• (3, -5)

• (-5, 3)

• (5, -3)

• (-3, 5)

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

• By the sign of the coefficient of X

• By the value of P

• By the sign of the coefficient of Y

• By the vertex coordinates

What is the focus of the parabola?

• (5, 3 1/8)

• (-5, 3 1/8)

• (5, 2 7/8)

• (-5, 2 7/8)

What is the equation of the directrix?

• X = 3 1/8

• Y = 3 1/8

• X = 2 7/8

• Y = 2 7/8