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avatar+1348 

Help, I can't get this

 

There exist constants a, h  and k such that

3x^2 + 12x + 4 - 2x^2 + 16x - 25 = a(x - h)^2 + k
for all real numbers  Enter the ordered triple (a,h,k).

 Apr 25, 2023
 #1
avatar+2668 
+1

Simplify the left-hand side to x2+28x21.

 

Now, notice that the right-hand side is just vertex form. This means that a is the coefficient of the x2 term (in this case it's 1) and that (h,k) is the vertex. 

 

The vertex is located at x=b2a=14. Substituting this in gives us (14)2+28(14)21=217. So, the vertex is (14,217).

 

Thus, the ordered triple is just (1,14,217)

 Apr 25, 2023

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