If we express 3x^2 - 6x - 2 in the form a(x - h)^2 + k, then what is a + h + k?
This is clearly an exercise in completing the square.
3x^2 - 6x - 2
3(x^2-2x) - 2
now add and subtract 3, leaving the value unchanged:
3(x^2-2x+1) - 2 - 3
3(x-1)^2 - 5
To express the quadratic expression 3x^2 - 6x - 2 in the form a(x - h)^2 + k, we need to complete the square.
Step 1: First, factor out the coefficient of x^2 as a common factor:
3x^2 - 6x - 2 = 3(x^2 - 2x) - 2
Step 2: To complete the square, take half of the coefficient of x (-2 in this case), square it, and add it inside the parentheses:
3(x^2 - 2x + (-2/2)^2) - 2 = 3(x^2 - 2x + 1) - 2
Step 3: Simplify the expression inside the parentheses:
3(x - 1)^2 - 2
Now we have the expression in the desired form.
By comparing this expression with the given form a(x - h)^2 + k, we can see that a = 3, h = 1, and k = -2.
To find a + h + k:
a + h + k = 3 + 1 + (-2) = 2.
Therefore, a + h + k is equal to 2.