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 rightward.

To find the axis of symmetry, $y=\frac{-b}{2a}$

So, $y=0$.

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.