Question

cises 12.4 Slete the following: Find the intercepts and domain and perform the symmetry test on each parabola with equation: Graph the vertex, focus, and endpoints of the latus in problem 1. (a) y2 = 8x (c) y2 = - 4x (b) x² = 8y (d) x² = -4y

Answer 1

The y-intercept is given by the value of y when x = 0, and the x-intercept is given by the value of x when y = 0.

The domain is all values of x the function can assume in order to y exist.

The axis of symmetry is the axis where the function is mirrowed.

a) y² = 8x -> y = √(8x)

`\begin{gathered} \text{y-intercept:} \\ x=0\to y^2=0\to y=0 \\ \text{x-intercept:} \\ y=0\to x=0 \\ \text{Domain: all real numbers} \\ \text{Axis of symmetry: }x=0 \end{gathered}`

b) x² = 8y

`\begin{gathered} \text{ y-intercept:} \\ x=0\to y=(0)/(8)=0 \\ \text{ x-intercept:} \\ y=0\to x^2=0\to x=0 \\ \text{Domain: all real numbers} \\ \text{Axis of symmetry: }x=0 \end{gathered}`

c) y² = -4x -> y = √(-4x)

`\begin{gathered} \text{ y-intercept:} \\ x=0\to y^2=0\to y=0 \\ \text{ x-intercept:} \\ y=0\to x=0 \\ \text{Domain: }x\le0 \\ \text{Axis of symmetry: }y=0 \end{gathered}`

d) x² = -4y

`\begin{gathered} \text{ y-intercept:} \\ x=0\to y=(0)/(-4)=0 \\ \text{ x-intercept:} \\ y=0\to x^2=0\to x=0 \\ \text{Domain: all real numbers} \\ \text{Axis of symmetry: }x=0 \end{gathered}`