Question

graph the function.
\\( r(x) = \

$$\begin{cases} \\,\\,\\,x^2 - 4 & \\text{for } x \\leq 2 \\\\ 5x - 10 & \\text{for } x > 2 \\end{cases}$$

\\)
part: 0 / 5
part 1 of 5
the first rule defines a \\( \boldsymbol{\text{select}} \\) with vertex \\( (\boldsymbol{\square}, \boldsymbol{\square}) \\).

Explanation:

Step1: Identify first rule's function type

The first rule is $r(x)=x^2 - 4$ for $x\leq2$, which is a quadratic function in the form $y=x^2 + k$.

Step2: Find vertex of the quadratic

For $y=x^2 + k$, the vertex is at $(0, k)$. Here $k=-4$, so vertex is $(0, -4)$.

Step3: Confirm function category

A quadratic function is a parabola.

Answer:

The first rule defines a parabola with vertex $(0, -4)$.