Answer:
Ok, "steeper than y = x^2" means that the function grows "faster" than y = x^2. and we can look at this by looking at the derivates, if the derivate is larger, then it is steeper.
The derivate of y = x^2 is: y´= 2x.
Now let's look at the other functions.
a) y = (1/2)*x^2
the derivate is:
y' = 2*(1/2)*x = x
this function is less steep than y = x^2
b) y = -x^2
the derivate is:
y' = -2x
So we have, in absolut value, exactly the same than for y = x^2.
The difference is that here the function decays instead of growing, so this is "less steep than y = x^2)
c) y = (2x)^2 = 4*x^2
the derivate is:
y´= 2*4*x = 8*x
this is steeper than y = x^2-
d) y = 2x^2
the derivate is:
y´= 2*2*x = 4x.
this is steeper than y = x^2
e) y = (x/2)^2 = (1/4)*x^2
the derivat is:
y' = (2/4)*x = (1/2)*x
so this is lees steep than y = x^2
