what is the x - intercept of the graph of the function (f(x)=x^{2}-16x + 64)?\n(-8, 0)\n(0, 8)\n(8, 0)\n(0…

Explanation:

Step1: Recall x - intercept definition

The x - intercept is found by setting (y = f(x)=0). So we set (x^{2}-16x + 64=0).

Step2: Factor the quadratic equation

We know that (x^{2}-16x + 64=(x - 8)^{2}) since ((a - b)^2=a^{2}-2ab + b^{2}), here (a = x) and (b = 8). So ((x - 8)^{2}=0).

Step3: Solve for x

Taking the square - root of both sides, we get (x-8 = 0), which gives (x = 8). The y - coordinate of the x - intercept is 0. So the x - intercept is the point ((8,0)).

Answer:

C. ((8,0))