Find the x-intercepts for the parabola whose equation is given.If the x-intercepts are irrational, round your answers to the nearest tenth. y=-x^2+17x-72 A. (-8,0) and (-9,0) ) B. (8,0) and (9,0) C. (8,0) and (-9,0) D. There are no x-intercepts.

To find the x-intercepts of the parabola, we need to set y equal to 0 and solve for x.<br /><br />$0=-x^{2}+17x-72$<br /><br />We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we will use the quadratic formula:<br /><br />$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$<br /><br />where a, b, and c are the coefficients of the quadratic equation. In our case, a = -1, b = 17, and c = -72.<br /><br />$x=\frac{-17\pm\sqrt{17^2-4(-1)(-72)}}{2(-1)}$<br /><br />$x=\frac{-17\pm\sqrt{289-288}}{-2}$<br /><br />$x=\frac{-17\pm\sqrt{1}}{-2}$<br /><br />$x=\frac{-17\pm1}{-2}$<br /><br />So, the x-intercepts are:<br /><br />$x_1=\frac{-17+1}{-2}=8$<br /><br />$x_2=\frac{-17-1}{-2}=9$<br /><br />Therefore, the correct answer is B. $(8,0)$ and $(9,0)$.