Answer
Vertex: $(-3/2, -81/4)$
Opens upward
x-intercepts: -6, 3
y-intercept: -18
Work Step by Step
$f(x)=x^2+3x-18$
$y=x^2+3x-18$
$(3/2)^2$
$9/4$
$y=x^2+3x-18$
$y=x^2+3x-18+9/4-9/4$
$y=x^2+3x+9/4-81/4$
$y=(x+3/2)^2-81/4$
Vertex: $(-3/2, -81/4)$
Opens upward
$x=0$
$f(x)=x^2+3x-18$
$f(0)=0^2+3*0-18$
$f(0)=0+0-18$
$f(0)=-18$
$y=0$
$y=(x+3/2)^2-81/4$
$0+81/4=(x+3/2)^2-81/4+81/4$
$0+81/4=(x+3/2)^2$
$81/4=(x+3/2)^2$
$\sqrt {81/4}=\sqrt {(x+3/2)^2}$
$±9/2=x+3/2$
$9/2=x+3/2$
$9/2-3/2=x+3/2-3/2$
$6/2=x$
$3=x$
$-9/2=x+3/2$
$-9/2-3/2=x+3/2-3/2$
$-12/2=x$
$-6=x$
x-intercepts: -6, 3
y-intercept: -18
