Learn how to graph an ellipse by re writing the equation from completing the square

The video tutorial explains how to graph an ellipse by converting its equation into vertex form. It covers completing the square to create perfect square trinomials, factoring, and simplifying the equation. The tutorial then demonstrates how to graph the ellipse by identifying the center, vertices, co-vertices, and foci, and concludes with a summary of the process.

What is the first step in graphing an ellipse from its equation?

• Find the length of the major axis

• Convert the equation to vertex form

• Identify the foci

• Determine the eccentricity

When completing the square, what must be true about the coefficient of the quadratic terms?

• It must be zero

• It must be a prime number

• It must be one

• It must be even

What is the purpose of adding constants to both sides of the equation when completing the square?

• To simplify the quadratic term

• To eliminate the linear term

• To balance the equation

• To change the axis of symmetry

In the standard form of an ellipse, what does the denominator under the x-term represent?

• The center of the ellipse

• The square of the semi-major axis

• The distance to the foci

• The length of the minor axis

How do you determine the center of an ellipse from its equation in standard form?

• By using the coefficients of the x and y terms

• By calculating the average of the vertices

• By identifying the values of h and k

• By finding the midpoint of the foci

What is the relationship between a^2, b^2, and c^2 in an ellipse?

• b^2 = a^2 + c^2

• a^2 = b^2 + c^2

• c^2 = a^2 - b^2

• a^2 = c^2 - b^2

How are the co-vertices of an ellipse determined?

• By adding and subtracting b from the x-coordinate of the center

• By adding and subtracting b from the y-coordinate of the center

• By finding the midpoint between the vertices

• By using the distance formula

What is the significance of the foci in an ellipse?

• They are the fixed points from which the sum of distances to any point on the ellipse is constant

• They are used to calculate the eccentricity

• They are the points where the ellipse is widest

• They determine the length of the major axis

Which axis is the major axis if the larger denominator is under the x-term?

• Vertical

• Horizontal

• Diagonal

• Undefined

What is the role of the center in graphing an ellipse?

• It determines the length of the minor axis

• It is the starting point for plotting vertices and co-vertices

• It is the point of intersection of the axes

• It is the midpoint of the major axis