Question

What are the y and x intercepts of y=3(x-6)²-9 and y=-2(x+5)²+3 .. Thanks

Answer 1

1.

`y=3(x-6)^2-9 \\ \\ \hbox{x-intercept - y=0} \\ 0=3(x-6)^2-9 \\ 9=3(x-6)^2 \ \ \ |/ 3 \\ 3=(x-6)^2 \\ √(3)=√((x-6)^2) \\ \pm √(3)=x-6 \\ \pm √(3)+6=x \\ x=6+√(3) \ \lor \ x=6-√(3)} \\ \\ \hbox{y-intercept - x=0} \\ y=3(0-6)^2-9 \\ y=3 * (-6)^2-9 \\ y=3 * 36-9 \\ y=108-9 \\ y=99 \\ \\ \boxed{\hbox{x-intercepts: } 6+√(3) \hbox{ and } 6-√(3)} \\ \boxed{\hbox{y-intercept: } 99}`

2.

`y=-2(x+5)^2+3 \\ \\ \hbox{x-intercept - y=0} \\ 0=-2(x+5)^2+3 \\ -3=-2(x+5)^2 \ \ \ |/ (-2) \\ (3)/(2)=(x+5)^2 \\ \sqrt{(3)/(2)}=√((x+5)^2) \\ \pm \sqrt{(3)/(2)}=x+5 \\ \pm \sqrt{(3)/(2)}-5=x \\ x=\sqrt{(3)/(2)}-5 \ \lor \ x=-\sqrt{(3)/(2)}-5 \\ \\ \hbox{y-intercept - x=0} \\ y=-2(0+5)^2+3 \\ y=-2 * 5^2 +3 \\ y=-2 * 25+3 \\ y=-50+3 \\ y=-47 \\ \\ \boxed{\hbox{x-intercepts: } \sqrt{(3)/(2)}-5 \hbox{ and } -\sqrt{(3)/(2)}-5} \\ \boxed{\hbox{y-intercept: } -47}`