Question

Make an X and Y table for the following function with all the points.

Answer 1

See below

Explanation:

To create an X and Y table for the function f(x) = -x² + 4, we can choose a set of values for x, calculate the corresponding f(x) values, and organize them into a table. Here's a representation of the table:

`\boxed{ \begin{array}c x & f(x) \\ -2 & -x^2 + 4 = -4 + 4 = 0 \\ 0 & -x^2 + 4 = 0 + 4 = 4 \\ 1 & -x^2 + 4 = -1 + 4 = 3 \\ 2 & -x^2 + 4 = -4 + 4 = 0 \\ \end{array}}`

In order to graph it, plot the value and join them.

See Attachment

This graph shows the parabolic shape of the function f(x) = -x² + 4, with its maximum value at x = 0, f(x) = 4, and symmetrically decreasing values as x moves away from 0.