solve $-8=-x^{2}-4$ by graphing. select the solution(s).\nno real solution $x=-8$ $x=-7$ $x=-6$…

solve $-8=-x^{2}-4$ by graphing. select the solution(s).\nno real solution $x=-8$ $x=-7$ $x=-6$ $x=-5$\n$x=-4$ $x=-3$ $x=-2$ $x=-1$ $x=0$\n$x=1$ $x=2$ $x=3$ $x=4$ $x=5$\n$x=6$ $x=7$ $x=8$ $x=9$ $x=10$

solve $-8=-x^{2}-4$ by graphing. select the solution(s).\nno real solution $x=-8$ $x=-7$ $x=-6$ $x=-5$\n$x=-4$ $x=-3$ $x=-2$ $x=-1$ $x=0$\n$x=1$ $x=2$ $x=3$ $x=4$ $x=5$\n$x=6$ $x=7$ $x=8$ $x=9$ $x=10$

Answer

Explanation:

Step1: Rearrange the equation

Rearrange (-8=-x^{2}-4) to (x^{2}-4 = 0). The general form of a quadratic equation is (y = ax^{2}+bx + c). Here (a = 1), (b=0), (c=-4). The roots of the quadratic equation (ax^{2}+bx + c = 0) can be found by graphing (y=ax^{2}+bx + c) and finding the (x) - intercepts.

Step2: Analyze the quadratic function

For the function (y=x^{2}-4), we know that (y=(x + 2)(x - 2)) (using the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)), here (a=x) and (b = 2)). The (x) - intercepts of the graph (y=x^{2}-4) are the solutions of the equation (x^{2}-4=0). Set (y = 0), then ((x + 2)(x - 2)=0). Using the zero - product property ((ab = 0) implies (a=0) or (b = 0)), we have (x+2=0) or (x - 2=0). Solving (x+2=0) gives (x=-2), and solving (x - 2=0) gives (x = 2).

Answer:

(x=-2) and (x = 2)