Answer
Graph of given equation $2y - x^{2} = 1$ is sketched as -
Work Step by Step
Given equation-
$2y - x^{2} = 1$
To sketch graph of this equation, we can either use a graphing calculator or find some points on it to draw it as freehand curve as following-
Substituting $x = 0$ in given equation-
$2 y - 0 = 1$
i.e.
$ y = \frac{1}{2} = 0.5$
Hence a point $P (0, 0.5)$ lies on the curve.
Now
Substituting $x = 1$ in given equation-
$2 y - 1 = 1$
i.e.
$ 2y = 2$
Hence the point $Q (1, 1)$ lies on the curve.
Now
Substituting $x = -1$ in given equation-
$2 y -(-1)^{2} = 1$
i.e. $2 y - 1 = 1$
i.e.
$ 2y = 2$
i.e. $ y = 1$
Hence the point $R (-1, 1)$ lies on the curve.
Now
Substituting $x = 2$ in given equation-
$2 y - 4 = 1$
i.e.
$ 2y = 5$
i.e. $ y = 2.5$
Hence the point $S (2, 2.5)$ lies on the curve.
Now
Substituting $x = -2$ in given equation-
$2 y -(-2)^{2} = 1$
i.e. $2 y - 4 = 1$
i.e.
$ 2y = 5$
i.e. $ y = 2.5$
Hence the point $T (-2, 2.5)$ lies on the curve.
Now we will mark the points $P, Q, R, S $ and $T$ on the graph paper and join these points AS A FREEHAND CURVE to get the graph of given equation $2y - x^{2} = 1$
