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If we express 3x^2 - 6x + 2 + x^2 - 2x + 7 in the form a(x - h)^2 + k, then what is a + h + k?

 Jan 25, 2022
 #1
avatar+1632 
+5

(This will be a step by step explanation instead of using completing the square formulas/shortcuts)

First we must simplify the original expression.

4x28x+9 this expression looks cleaner.

 

Since we have to complete the square, we know a, the coefficient of x2 has to be 4.

 

If we open the parenthesis of (xh)2, we get x2+h22hx

Then since we are multiplying 4 to the expression, we have 4x2+4h28hx

 

h is a constant. if 8hx is the only value with x1, then 8h=8 in the original expression. Thus h=1.

 

The new expression 4x28x+4 has a difference of a positive 5 than the original expression 4x28x+9

Thus k=5.

 

Adding up our values, we have a + h + k = 4 + 1 + 5 = 10.

 

smiley

 Jan 26, 2022

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