Chapter 9.2, Problem 39HP

To determine

To find: The person whose graph is correct and explain.

Answer to Problem 39HP

Russell’s graph is correct.

Explanation of Solution

Given:

The equation is $\frac{1}{4}{y}^2+x=0$ .

Calculation:

Solve the equation $\frac{1}{4}{y}^2+x=0$ for $x$ .

  $\begin{array}{c}\frac{1}{4}{y}^2+x=0\\ x=-\frac{1}{4}{y}^2\end{array}$

Here, $a=-\frac{1}{4}$ which is less than 0 so it opens to the left for a sideways parabola. Vertex is $\left(h,k\right)=\left(0,0\right)$ .

Check the directrix.

  $\begin{array}{c}x=h-\frac{1}{4a}\\ =0-\frac{1}{4\left(-0.25\right)}\\ =1\end{array}$

So, the distance from the vertex is 1. So the focus at $\left(-1,0\right)$ is also correct.

Therefore, Russell’s graph is correct.