1.
[tex]y=3(x-6)^2-9 \\ \\
\hbox{x-intercept - y=0} \\
0=3(x-6)^2-9 \\
9=3(x-6)^2 \ \ \ |\div 3 \\
3=(x-6)^2 \\
\sqrt{3}=\sqrt{(x-6)^2} \\
\pm \sqrt{3}=x-6 \\
\pm \sqrt{3}+6=x \\
x=6+\sqrt{3} \ \lor \ x=6-\sqrt{3}} \\ \\
\hbox{y-intercept - x=0} \\
y=3(0-6)^2-9 \\
y=3 \times (-6)^2-9 \\
y=3 \times 36-9 \\
y=108-9 \\
y=99 \\ \\
\boxed{\hbox{x-intercepts: } 6+\sqrt{3} \hbox{ and } 6-\sqrt{3}} \\
\boxed{\hbox{y-intercept: } 99}[/tex]
2.
[tex]y=-2(x+5)^2+3 \\ \\
\hbox{x-intercept - y=0} \\
0=-2(x+5)^2+3 \\
-3=-2(x+5)^2 \ \ \ |\div (-2) \\
\frac{3}{2}=(x+5)^2 \\
\sqrt{\frac{3}{2}}=\sqrt{(x+5)^2} \\
\pm \sqrt{\frac{3}{2}}=x+5 \\
\pm \sqrt{\frac{3}{2}}-5=x \\
x=\sqrt{\frac{3}{2}}-5 \ \lor \ x=-\sqrt{\frac{3}{2}}-5 \\ \\
\hbox{y-intercept - x=0} \\
y=-2(0+5)^2+3 \\
y=-2 \times 5^2 +3 \\
y=-2 \times 25+3 \\
y=-50+3 \\
y=-47 \\ \\ \boxed{\hbox{x-intercepts: } \sqrt{\frac{3}{2}}-5 \hbox{ and } -\sqrt{\frac{3}{2}}-5} \\ \boxed{\hbox{y-intercept: } -47}[/tex]
