Understanding Parabolas and Their Graphs

This video tutorial from MooMoo Math covers the final lesson on parabolas, a type of conic section. It explains the differences between vertical and horizontal parabolas, focusing on their equations and how to shift them using H and K values. The tutorial provides step-by-step instructions on graphing parabolas, including examples with different orientations and shifts. It also covers how to write the equation of a parabola in standard form by completing the square, offering practical examples to illustrate the process.

What is the primary difference between vertical and horizontal parabolas?

• Vertical parabolas open left or right, while horizontal parabolas open up or down.

• Vertical parabolas open up or down, while horizontal parabolas open left or right.

• Vertical parabolas have no vertex, while horizontal parabolas do.

• Vertical parabolas are always wider than horizontal parabolas.

In the equation of a parabola, what role do the H and K values play?

• They change the direction the parabola opens.

• They shift the vertex of the parabola.

• They affect the steepness of the parabola.

• They determine the width of the parabola.

How do you determine the direction a parabola opens based on its equation?

• By the length of the axis of symmetry.

• By the distance between the focus and directrix.

• By the value of H and K.

• By the sign of the coefficient of the squared term.

What is the focus of a parabola with the equation y^2 = 16x?

• (0, 4)

• (4, 0)

• (0, -4)

• (-4, 0)

When graphing a parabola, what does the directrix represent?

• A line that the parabola never touches.

• A line that is perpendicular to the axis of symmetry.

• The line of symmetry for the parabola.

• A line that is parallel to the axis of symmetry.

In the equation y - 2^2 = -16(x - 5), what is the vertex of the parabola?

• (-5, -2)

• (-2, -5)

• (2, 5)

• (5, 2)

What is the first step in completing the square for a parabola's equation?

• Add the same value to both sides of the equation.

• Get the squared term and its like term on one side.

• Factor out the greatest common factor.

• Move all terms to one side of the equation.

How do you find the vertex of a parabola in standard form?

• By identifying the coefficients of the squared term.

• By using the values of H and K in the equation.

• By calculating the midpoint of the focus and directrix.

• By finding the intersection of the axis of symmetry and the directrix.

What is the vertex of the parabola given by the equation y^2 + 6y = 2x - 9?

• (-3, 0)

• (0, -3)

• (3, 0)

• (0, 3)

What is the value of p if 4p equals 8 in a parabola's equation?

• 1

• 4

• 2

• 3