13. What are the solutions of the equation x^2−16=0? Use a graph of the related function.

Answer 1

The solutions of the equation x^2 - 16 = 0 can be found by setting the equation equal to zero and solving for x:

x^2 - 16 = 0
x^2 = 16
x = ±4

So, the solutions of the equation are x = 4 and x = -4.

To graph the related function y = x^2 - 16, we plot the points (4, 0) and (-4, 0) on a Cartesian plane and draw a parabola passing through these points. The graph of the function will be a parabola opening upwards, with the x-intercepts at x = 4 and x = -4.

The graph of the function y = x^2 - 16 is shown below:

image: https://www5b.wolframalpha.com/Calculate/MSP/MSP34621f4cfa8aa9c16e00004g0b3f3d7fd93d57fi?MSPStoreType=image/gif&s=39

The x-intercepts of the graph correspond to the solutions of the equation x^2 - 16 = 0, which are x = 4 and x = -4.