what are the x - intercepts of the function $f(x)=-x^{2}-x + 2$?\n(-2, 0) and (1, 0)\n(2, 0) and (1…

what are the x - intercepts of the function $f(x)=-x^{2}-x + 2$?\n(-2, 0) and (1, 0)\n(2, 0) and (1, 0)\n(-2, 0) and (-1, 0)\n(0, -2) and (0, 1)

what are the x - intercepts of the function $f(x)=-x^{2}-x + 2$?\n(-2, 0) and (1, 0)\n(2, 0) and (1, 0)\n(-2, 0) and (-1, 0)\n(0, -2) and (0, 1)

Answer

Explanation:

Step1: Set the function equal to 0.

To find the x - intercepts, we set (f(x)=0), so (-x^{2}-x + 2=0). Multiply through by - 1 to get (x^{2}+x - 2=0).

Step2: Factor the quadratic equation.

We factor (x^{2}+x - 2) as ((x + 2)(x - 1)=0).

Step3: Solve for x.

Using the zero - product property, if (ab = 0), then (a = 0) or (b = 0). So (x+2=0) gives (x=-2) and (x - 1=0) gives (x = 1). The x - intercepts are written as points ((-2,0)) and ((1,0)).

Answer:

A. ((-2,0)) and ((1,0))