Answer:

Step-by-step explanation:
We have the function: 

And we want to find x=d for which the minimum/maximum value will occur. 
Notice that our function is a quadratic in factored form.
Remember that the minimum/maximum value always occurs at the vertex point. 
And remember that the x-coordinate of the vertex is the axis of symmetry. 
Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic. 
Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots. 
Our factors are <em>(x-2) </em>and <em>(x-1)</em>. 
Therefore, our roots/zeros are <em>x=1, 2</em>. 
So, the average of them are: 

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>. 
Alternative Method: 
Of course, we can also expand to confirm our answer. So: 

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur. 
And the formula for the vertex is: 

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields: 

Confirming our answer.