Question

Find the y- intercept and domain and perform the symmetry test on each parabola with equationy^2 = 8x

Answer 1

Answer:

y-intercept = (0, 0)

Domain = x > 0 (positive real numbers)

Axis of symmetry: y = 0

Explanations:

The equation of the parabola given is:

`y^2\text{ = 8x}`

The general equation of a parabola when the directrix is parallel to the y-axis is:

`y^2\text{ = 4ax}`

Comparing the two equations:

4a = 8

a = 8/4

a = 2

To find the y -intercept, let x = 0

`\begin{gathered} y^2\text{ = 8(0)} \\ y^2\text{ = 0} \\ y\text{ = 0} \end{gathered}`

y intercept = (0, 0)

The domain is the set of all real numbers greater than 0, because y will be finite for all values of x greater than 0

To perform the symmetry test:

The axis of symmetry is the line that passes through the vertex and focus, which is y=0