Vertex Form and Parabola Properties

The video tutorial explains how to match equations of parabolas to their corresponding graphs. It covers the standard and vertex forms of parabolas, detailing the vertical and horizontal axes of symmetry. The tutorial provides step-by-step solutions for four equations, determining the vertex and axis of symmetry for each, and matching them to the correct graphs.

What is the standard form of a parabola as defined in the textbook?

• y = a(x - h)^2 + k

• x = ay^2 + by + c

• y = ax^2 + bx + c

• x = a(y - k)^2 + h

In the vertex form of a parabola, what does the 'h' represent?

• The y-coordinate of the vertex

• The distance to the focus

• The x-coordinate of the vertex

• The axis of symmetry

If 'a' is positive in the equation y = a(x - h)^2 + k, how does the parabola open?

• To the right

• To the left

• Downwards

• Upwards

What is the axis of symmetry for the equation x = a(y - k)^2 + h?

• x = h

• y = k

• x = k

• y = h

In the equation x = a(y - k)^2 + h, what does the absolute value of 'p' indicate?

• The slope of the parabola

• The width of the parabola

• The distance from the vertex to the focus

• The height of the parabola

For the equation x = 3(y + 1)^2 - 2, what is the vertex?

• (2, -1)

• (-2, 1)

• (-2, -1)

• (2, 1)

Which graph corresponds to the equation x = 3(y - 1)^2 - 2?

• Graph A

• Graph B

• Graph C

• Graph D

For the equation y = 3(x + 2)^2 + 1, what is the vertex?

• (2, -1)

• (-2, -1)

• (2, 1)

• (-2, 1)

Which graph corresponds to the equation y = 3(x - 2)^2 + 1?

• Graph D

• Graph B

• Graph A

• Graph C

What is the common feature of the parabolas in equations 3 and 4?

• They open to the left

• They open to the right

• They open downwards

• They open upwards