Answer:
Simplify them to the lowest.
What's the GCF( Greatest Common Factor). It's 8. So divide both sides by 8.
24/8 = 3
56/8 = 7
so it's
3 dogs to 7 cats
Step-by-step explanation:
Te x intercepts are where the graph crosses the x axis or wher y=0
the y intercept is where the graph crosses the y axis or where x=0
to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a
so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8
vertex is (-2,-8)
intercepts
x intercept is where y=0
0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)
yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)
vertex at (-2,-8)
xints at x=

and

or at the points

and

yint at y=7 or at (7,0)
BC is greater than AC is correct. If you need help with the construction, feel free to ask.
And maybe you're not clear with the options, because you've written BC two times which is necessarily not an answer/option.