Questions: Sketch the graph of the parabola by using only the vertex and the y-intercept. Check the graph using a graphing calculator. R=v^2+6v Use the graphing tool to graph the parabola. Click to enlarge graph

Sketch the graph of the parabola by using only the vertex and the y-intercept. Check the graph using a graphing calculator.

R=v^2+6v

Use the graphing tool to graph the parabola.

Click to enlarge graph

Transcript text: Sketch the graph of the parabola by using only the vertex and the $y$-intercept. Check the graph using a graphing calculator. \[ R=v^{2}+6 v \] Use the graphing tool to graph the parabola. Click to enlarge graph

Solution

Solution Steps

Step 1: Rewrite the equation in vertex form

The given equation is $R = v^2 + 6v$. To rewrite this in vertex form, we complete the square:

$R = v^2 + 6v$ $R = (v^2 + 6v + 9) - 9$ $R = (v+3)^2 - 9$

Step 2: Find the vertex

The vertex form of a parabola is given by $R = a(v-h)^2 + k$, where $(h,k)$ is the vertex. In our case, $h = -3$ and $k = -9$. So, the vertex is at $(-3, -9)$.

Step 3: Find the y-intercept

The y-intercept occurs when $v=0$. Substituting $v=0$ into the equation gives us:

$R = (0)^2 + 6(0) = 0$

So the y-intercept is at $(0,0)$.