Question

Make a table of values, and sketch the graph of the equation.

$y=3-x^2$

Short answer

The graph of the equation$y=3-x^2$ is provided below.

Step-by-step solution

Step 1. Apply the concept of coordinates.

The set of all points$\left(x,y\right)$ in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Step 2. Construct a table of values.

Consider the provided equation$y=3-x^2$

Consider real values for x and corresponding to it find the values of y.

$\begin{array}{ccc}x& y=3-x^2& \left(x,y\right)\\ -2& -1& \left(-2,-1\right)\\ -1& 2& \left(-1,2\right)\\ 0& 3& \left(0,3\right)\\ 1& 2& \left(1,2\right)\\ 2& -1& \left(2,-1\right)\end{array}$

Step 3. Graph the equation.

Plot the ordered pairs on the Cartesian plane to obtain the graph of the equation $y=3-x^2$.