Understanding Parabolas with Horizontal Axes of Symmetry

This lesson explores the graph of a parabola in the form x = a(y-k)^2 + h, focusing on how the parameters a, h, and k affect its shape and position. The parabola's axis of symmetry is horizontal, and its vertex is at (h, k). The value of a determines the direction and width of the parabola, with positive a opening to the right and negative a to the left. The absolute value of a affects the parabola's width, with values greater than 1 making it narrower and values between 0 and 1 making it wider. The parameter h shifts the graph horizontally, while k shifts it vertically.

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

• y = h

• x = k

• y = k

• x = h

If 'a' is greater than zero, in which direction does the parabola open?

• To the right

• Downwards

• Upwards

• To the left

How does the graph of a parabola shift when 'h' is positive?

• To the left

• To the right

• Downwards

• Upwards

What happens to the parabola when 'h' is negative?

• It shifts to the left

• It shifts to the right

• It shifts downwards

• It shifts upwards

When 'k' is positive, how does the parabola move?

• To the left

• Upwards

• To the right

• Downwards

If 'k' is negative, what is the effect on the parabola?

• It moves to the left

• It moves to the right

• It moves upwards

• It moves downwards

What is the effect on the parabola when 'a' is greater than 1?

• It shifts downwards

• It becomes wider

• It becomes narrower

• It shifts upwards

How does the parabola change when 'a' is between 0 and 1?

• It shifts to the left

• It becomes narrower

• It shifts to the right

• It becomes wider

What happens to the parabola when 'a' is negative?

• It becomes narrower

• It becomes wider

• It opens to the left

• It opens to the right

When 'a' is negative and its absolute value is greater than 1, what is the effect on the parabola?

• It shifts downwards

• It shifts upwards

• It becomes narrower

• It becomes wider