Answer
Vertex: $(1/2, -25/2)$
Opens upward
x-intercepts: -3, 4
y-intercept: -12
Work Step by Step
$f(x)= x^2-x-12$
Vertex: $x=-b/2a$
$x=-(-1)/2*1$
$x=1/2$
$f(x)= x^2-x-12$
$f(1/2)= (1/2)^2-(1/2)-12$
$f(1/2)=1/4-1/2-12$
$f(1/2)=-25/2$
Vertex: $(1/2, -25/2)$
Opens upward
$x=0$
$f(x)= x^2-x-12$
$f(0)= 0^2-0-12$
$f(0)= 0-0-12$
$f(0)= -12$
$y=0$
$y=x^2-x-12$
$0=x^2-x-12$
$0=x^2-4x+3x-12$
$0=x(x-4)+3(x-4)$
$0=(x-4)(x+3)$
$x-4=0$
$x-4+4=0+4$
$x=4$
$x+3=0$
$x+3-3=0-3$
$x=-3$
x-intercepts: -3, 4
y-intercept: -12
