Answer
Vertex: $(-5,-10)$
Opens upward
x-intercepts: -1.8, -8.2
y-intercept: 15
Work Step by Step
$f(x)=x^2+10x+15$
$y=x^2+10x+15$
$y=x^2+10x+(10/2)^2-(10/2)^2+15$
$y=x^2+10x+5^2-5^2+15$
$y=(x+5)^2-25+15$
$y=(x+5)^2-10$
Vertex: $(-5,10)$
Coefficient of $x^2$ is positive, so graph opens up
$y=0$
$y=(x+5)^2-10$
$0=(x+5)^2-10$
$0+10=(x+5)^2-10+10$
$10=(x+5)^2$
$\sqrt {10}=\sqrt {(x+5)^2}$
$±\sqrt 10 = x+5$
$±3.16 = x+5$
$3.16=x+5$
$3.16-5=x+5-5$
$-1.84 = x$
$x=-1.8$
$-3.16=x+5$
$-3.16-5=x+5-5$
$-8.16=x$
$x=-8.2$
$x=0$
$y=(x+5)^2-10$
$y=(0+5)^2-10$
$y=5^2-10$
$y=25-10$
$y=15$