Determine whether the statement is true or false. If the statement is false, explain why. The graph of $y=x^{2}-6$ has two $x$-intercepts. Select the correct choice below. A. True; the graph of $y=x^{2}-6$ has two $x$-intercepts. B. False; the graph of $y=x^{2}-6$ has no $x$-intercepts. C. False; the graph of $y=x^{2}-6$ has only one $x$-intercept. D. False; the graph of $y=x^{2}-6$ has three $x$-intercepts.

Step 1 ：The x-intercepts of a graph are the points where the graph intersects the x-axis. This happens when y = 0. So, to find the x-intercepts of the graph of \(y=x^{2}-6\), we need to solve the equation \(x^{2}-6=0\) for x.

Step 2 ：This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula, which is \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\), where a, b, and c are the coefficients of the quadratic equation in the form \(ax^{2}+bx+c=0\). In this case, a = 1, b = 0, and c = -6.

Step 3 ：Substituting the values of a, b, and c into the quadratic formula, we get two solutions for x: \(x = \frac{-0 \pm \sqrt{0^{2}-4(1)(-6)}}{2(1)}\), which simplifies to \(x = \frac{\pm \sqrt{24}}{2}\).

Step 4 ：The roots of the equation \(x^{2}-6=0\) are approximately 2.45 and -2.45. These are the x-coordinates of the points where the graph of \(y=x^{2}-6\) intersects the x-axis.

Step 5 ：Therefore, the graph of \(y=x^{2}-6\) has two x-intercepts.

Step 6 ：Final Answer: \(\boxed{\text{A. True; the graph of } y=x^{2}-6 \text{ has two x-intercepts.}}\)