Answer:
1-2a is the largest for -1 > a > -2.41
a^2 is the largest for -2.41 > a.
Explanation:
We want to find the expression with the largest value.
Remember that the sign is important here, because:
1 is larger than -10
So we will look at the expressions that, when evaluated in a negative number, give a positive number.
The only two options in the case:
a < -1
are:
1-2a
and
a^2
So we have a linear equation and a quadratic equation.
We know that quadratic equations grow a lot faster than linear equations for all values larger than 1 (or minus one, because the sign does not matter).
if -1 < a < 1, a quadratic function grows really slow, but this is not the case.
So from now, we can guess that a^2 is larger.
But let's solve it graphically.
Let's define two functions:
f(a) = 1 - 2*a
g(a) = a^2
Now we can graph these two, and look at the region a < -1, and see which one is larger.
in the image, you can see that there is a small region from:
-1 > a > -2.41
Where the linear equation is larger, and for:
a < -2.41
The quadratic equation is larger.