Find the equation vertex (5, 2) Focus (3, 2)

The video tutorial guides students through the process of identifying the vertex and focus of a parabola, determining its orientation, and deriving the standard form of a horizontal parabola. It includes plotting points, understanding the role of the focus, and calculating the value of P to complete the equation.

What is the first step in solving the problem of finding the standard form of a parabola?

• Calculate the distance between the vertex and the focus.

• Plot the given points on a graph.

• Find the directrix of the parabola.

• Determine the axis of symmetry.

How can you determine if a parabola is horizontal or vertical?

• By calculating the slope of the line through the vertex and focus.

• By checking the distance between the vertex and the focus.

• By observing the direction of the parabola's opening.

• By analyzing the coordinates of the vertex and focus.

What is the standard form equation for a horizontal parabola?

• y^2 = 4p(x - h)

• x^2 = 4p(x - h)

• x^2 = 4p(y - k)

• y^2 = 4p(y - k)

What value of 'P' is used in the equation if the distance between the vertex and the focus is 2?

• 1

• 8

• 2

• 4

What is the final standard form of the parabola given the vertex (5, 2) and focus (3, 2)?

• y^2 = 4(x - 5)

• x^2 = 8(y - 2)

• y^2 = 8(x - 5)

• x^2 = 4(y - 2)