Question

ercises 12.4 Find the intercepts and domain and perform the symmetry test on each parabola with equation: the following: aplete (a) y? = 8x (e) y = - 4x (b) x = 8y (d) x = - 4y he vertex, focus, and endpoints of the

Answer 1

We have the equation a)

`\begin{gathered} y^2=8x\text{ } \\ y=\sqrt[]{8x} \end{gathered}`

The domain of a function is the set of all possible inputs for the function. In this case, as a root can not take a negative number, x can not take negative values. The domain would be from 0 to positive infinite.

The intercepts are calculated:

Intercept in y-axis y=0, we replace in the equation and solve for x:

`\begin{gathered} 0=8x \\ x=0 \end{gathered}`

Intercept in x-axis x=0, we replace in the equation and solve for y:

`\begin{gathered} y^2=8\cdot0 \\ y=0 \end{gathered}`

Only one intercept in the parabola (0,0)

Symmetry:

We check for symmetry about the x-axis, replacing the y for -y:

`\begin{gathered} (-y)^2=8x \\ y^2=8x \end{gathered}`

This is identical to the original equation, so we have symmetry about the x-axis.

Now we check for symmetry about the y-axis, replacing in the equation the x for -x:

`\begin{gathered} y^2=8(-x) \\ y^2=-8x \end{gathered}`

This is not identical to the original equation since the sign of 8x changes to negative, this means there is no symmetry about the y-axis.