Question

Identify the orientation of the axes of symmetry of the standard form equations of the parabola given below.

Answer 1

`\sf (x -h)^2 = 4p(y-k) \textsf{ vertical }`

`\sf (y-k)^2 = 4p(x -h) \textsf{ horizontal }`

Explanation:

The orientation of the axis of symmetry of a parabola in standard form can be determined by the form of the equation.

If the equation is in the form of
`\tt y = a(x - h)^2 + k`, then the axis of symmetry is vertical, and the equation of the axis is x=h.

If the equation is in the form of
`\tt x = a(y - k)^2 + h,` then the axis of symmetry is horizontal, and the equation of the axis is y=k.

The equations you provided are:

`\tt (x -h)^2 = 4p(y-k)`

(y-k)^2 = 4p(x − h)

In the first equation, the x term is squared, so the axis of symmetry is Vertical.

In the second equation, the y term is squared, so the axis of symmetry is Horizontal.

Therefore, the answers are:

`\sf (x -h)^2 = 4p(y-k) \textsf{ vertical }`

`\sf (y-k)^2 = 4p(x -h) \textsf{ horizontal }`