Chapter 8, Problem 19RE

Solution

To find:The correct graph for the given equation $x^2=-4y$ .

The correct graph for the equation $x^2=-4y$ is option (c).

Given information:

The equation is $x^2=-4y$ .

Calculation:

The given equation is of the form

  $x^2=4py$

This is the standard equation of parabola with vertex $\left(0,0\right)$ that opens upward or downward.

Comparing $x^2=-4y$ with $x^2=4py$ gives

  $\begin{array}{c}4p=-4\\ p=-1\end{array}$

Since, $p=-1<0$ . So, the given parabola opens downward.

The graph of the equation $x^2=-4y$ is,

  

Therefore, the correct graph of the given equation $x^2=-4y$ is option (c).