Question

Solve x2 + 2 = 6 by graphing the related function.

Answer 1

Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.

Answer 2

Answer:

$x=-2,x=2$

Step-by-step explanation:

we have

$x^{2}+2=6$

we know that

The solution of the function is equivalent to solve the following system of equations

$y=x^{2}+2$ ------> equation A

$y=6$ ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are $(-2,6)$ and $(2,6)$

therefore

The solution of the given function are

$x=-2,x=2$