Question

What are the x-intercepts of the graph of the following equation ?

Answer 1

Answer:

           x-intercepts:  (-6, 0) ,  (2, 0)

Step-by-step explanation:

x-intercepts are points where y=0

$y = -x^2 - 4x + 12\\\\y=0\quad\iff\quad -x^2 - 4x + 12=0\\\\{}\qquad\quad\quad a=-1\,,\ b=-4\,,\ c=12\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(4)\pm\sqrt{(-4)^2-4\cdot(-1)\cdot12}}{2\cdot(-1)}=\dfrac{4\pm\sqrt{16+48}}{-2}\\\\x_1=\dfrac{4+\sqrt{64}}{-2}=\dfrac{12}{-2}=-6\ ,\quad x_2=\dfrac{4-8}{-2}=\dfrac{-4}{-2}=2$

x-intercepts:  (-6, 0) ,  (2, 0)