What are the two equations for a parabola in conic sections

The video tutorial explains graphing parabolas using quadratic equations in standard and vertex forms. It covers the importance of the axis of symmetry and vertex in graphing, and introduces equations for parabolas with vertical and horizontal axes of symmetry. The tutorial also discusses the role of the focus and directrix in defining parabolas, and how to adjust equations based on the orientation of the axis of symmetry.

What is the standard form of a quadratic equation used for graphing parabolas?

• Y = MX + B

• A(X - H)^2 + K

• AX^2 + BX + C

• X^2 + Y^2 = R^2

In the vertex form of a quadratic equation, what does the vertex represent?

• The slope of the parabola

• The intersection with the y-axis

• The midpoint of the parabola

• The highest or lowest point of the parabola

When the axis of symmetry is vertical, what determines if the parabola opens upwards or downwards?

• The sign of the distance from the vertex to the focus

• The value of the vertex

• The length of the directrix

• The coefficient of X

How do you modify the equation of a parabola when the axis of symmetry is horizontal?

• Divide the equation by the vertex

• Multiply the equation by 2

• Add a constant to the equation

• Swap X and Y in the equation

If P is positive in a horizontal axis of symmetry, which direction does the parabola open?

• To the left

• Upwards

• To the right

• Downwards