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?
(This will be a step by step explanation instead of using completing the square formulas/shortcuts)
First we must simplify the original expression.
4x2−8x+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 (x−h)2, we get x2+h2−2hx.
Then since we are multiplying 4 to the expression, we have 4x2+4h2−8hx.
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 4x2−8x+4 has a difference of a positive 5 than the original expression 4x2−8x+9.
Thus k=5.
Adding up our values, we have a + h + k = 4 + 1 + 5 = 10.