Conics Graphing an ellipse standard form by completing the square

The video tutorial guides students through the process of graphing equations by rewriting them into a standard form. It covers completing the square to create perfect square trinomials, converting equations to standard form, and determining the center and vertices of the graph. The tutorial concludes with graphing an ellipse using calculated values, emphasizing the importance of understanding the relationship between the center, vertices, and foci.

What is the first step in rewriting an equation to graph it?

• Multiply by a constant

• Add all terms to one side

• Rearrange terms to group x's and y's

• Subtract the constant term

What is the purpose of completing the square in an equation?

• To eliminate the constant term

• To create a perfect square trinomial

• To factor out the coefficient

• To simplify the equation

Why do we like perfect square trinomials?

• They make equations equal zero

• They eliminate the need for coefficients

• They can be factored into binomial squares

• They simplify to linear equations

What must be done to ensure the equation equals one?

• Divide by the largest coefficient

• Add a constant to both sides

• Divide by the constant term

• Multiply by a constant

How do you determine the orientation of the graph?

• By the sign of the coefficients

• By the larger denominator

• By the constant term

• By the sum of the coefficients

What is the center of the graph in this problem?

• (0, 0)

• (1, 4)

• (4, 1)

• (2, 3)

How do you find the vertices of the graph?

• By dividing the center by the square root of b squared

• By multiplying the center by a constant

• By adding and subtracting the square root of a squared from the center

• By adding the coefficients

What is the distance from the center to the foci?

• 4

• Square root of 8

• 2.8

• Square root of 24

What is the approximate value of the square root of 8?

• 2.5

• 3.2

• 3.0

• 2.8

What is the main goal when converting to vertex form?

• To simplify the coefficients

• To eliminate the y terms

• To ensure the equation equals one

• To find the x-intercepts