Question

Graph$x=-y^2$by using properties.

Short answer

The graph for the function $x=-y^2$is,

Step-by-step solution

Step 1 Given equation is,

$x=-y^2$.

Compare the given equation with $x=a{y}^2+by+c$.

we get, $a=-1$.

Since $a=-1$, the parabola opens leftward.

To find the axis of symmetry, $$\begin{gathered} y=\frac{-b}{2a} \\ y=0. \end{gathered}$$

The vertex is on the line $y=0$.

Step 2 Substitute y=0 in the given equation.

$x=0$.

So, the vertex is, $\left(0,0\right)$.

Since the vertex is $\left(0,0\right)$, both the $x$- and $y$intercepts are the point$\left(0,0\right)$. To graph the parabola we need more points.

Let us draw a table to choose values of $y$.

Step 3 Now find the symmetric points.

The points symmetric to $\left(-1,1\right)$and $\left(-4,2\right)$across the $y$-axis are, $\left(-1,-1\right)$and $\left(-4,-2\right)$.

Now plot the graph for the given function by using the known values.