Answer
Vertex: $(13/6, -289/12)$
Opens upward
x-intercepts: -2/3, 5
y-intercept: -10
Work Step by Step
$f(x)=3x^2-13x-10$
Vertex: $x=-b/2a$
$x=-(-13)/2*3$
$x=13/6$
$f(x)=3x^2-13x-10$
$f(13/6)=3(13/6)^2-13(13/6)-10$
$f(13/6)=3*169/36-169/6-10$
$f(13/6)=169/12-229/6$
$f(13/6)=169/12-458/12$
$f(13/6)=-289/12$
Vertex: $(13/6, -289/12)$
Opens upward
$x=0$
$f(x)=3x^2-13x-10$
$f(0)=3*0^2-13*0-10$
$f(0)=3*0-0-10$
$f(0)=0-10$
$f(0)=-10$
$y=0$
$f(x)=3x^2-13x-10$
$0=3x^2-13x-10$
$0=(3x+2)(x-5)$
$3x+2=0$
$3x+2-2=0-2$
$3x=-2$
$3x/3=-2/3$
$x=-2/3$
$x-5=0$
$x-5+5=0+5$
$x=5$
x-intercepts: -2/3, 5
y-intercept: -10
