Question

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

y = -x2 - 4x + 12

(Show work)

Answer 1

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

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=(-b\pm√(b^2-4ac))/(2a)=(-(4)\pm√((-4)^2-4\cdot(-1)\cdot12))/(2\cdot(-1))=(4\pm√(16+48))/(-2)\\\\x_1=(4+√(64))/(-2)=(12)/(-2)=-6\ ,\quad x_2=(4-8)/(-2)=(-4)/(-2)=2`

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