Question

Draw the graph of the given quadratic equations$y=\frac{1}{2}{x}^2-2$

Answer 1

The given quadratic equation is $y=\frac{1}{2}{x}^2-2$. When we substitute different values of $x$ in the equation $y=\frac{1}{2}{x}^2-2$ then value of $y$ changes accordingly.

When $x=0$ then

$y=\frac{1}{2}(0{)}^2-2=0-2=-2$

The point is $(0,-2)$

When $x=1$ then

$y=\frac{1}{2}(1{)}^2-2=\frac{1}{2}-2=-\frac{3}{2}$

The point is $(1,-\frac{3}{2})$

When $x=-1$ then

$y=\frac{1}{2}(-1{)}^2-2=\frac{1}{2}-2=-\frac{3}{2}$

The point is $(-1,-\frac{3}{2})$

Hence, the coordinates are $(0,-2)$, $(1,-\frac{3}{2})$ and $(-1,-\frac{3}{2})$and the graph of the quadratic equation $y=\frac{1}{2}{x}^2-2$ is as shown above.