Please help Without graphing, explain how you know the equation
y = - 1/2x^2 - 7 will be compressed
(compared to the parent function of y=x^2).

" because the coefficient of the x^2 term is less than 1 (between -1 and + 1)  

y = x^2 looks like a big U with the vertex (bottom) "kissing" the origin (0,0)

if you add 1 to the equation y = x^2 + 1 it shifts UP one  

if you subtract 3 y = x^2 -3 it shifts down three

if you change it to look like this y = (x+4)^2 it shifts (slides) to the LEFT 4 units..

note that this slide is opposite to the sign + 4 left slide , - 4 right slide...

NOW YOUR QUESTION if the coefficient is > 1  

y = 99 x^2 then the graph gets "skinny" goes up faster...

if it is less than one (between -1 past 0 to +1 ) then it flattens out

Bottom line here your coefficient is a "-1/2"  

so YOUR GRAPH IS A ∩ (goes downward) and is FLATTER than the normal ∪

I hope that this helps

Step-by-step explanation: