Solve 0 = (x – 4)2 – 1 by graphing the related function.

Question

What are the solutions to the equation?

–1 and 8
1 and 8
2 and 3
3 and 5

Answer 1

To solve the equation 0 = (x – 4)^2 – 1, we first need to rewrite it in the standard form of a quadratic equation:

0 = (x – 4)^2 – 1
0 = x^2 - 8x + 16 - 1
0 = x^2 - 8x + 15

Now, let's graph the related function y = x^2 - 8x + 15:

This is a parabolic function with a vertex at (4, 1).

To find the solutions to the equation, we need to find the x-intercepts of the graph, which represent the solutions to the equation.

By looking at the graph or by solving the quadratic equation x^2 - 8x + 15 = 0, we find that the solutions are x = 3 and x = 5.

Therefore, the solutions to the equation 0 = (x – 4)^2 – 1 are 3 and 5.