Answer:
Explanation:
To complete the square, we need to add and subtract a constant term that will allow us to write the function in the form f(x) = a(x + h)^2 + k. Here's how we can rewrite f(x) = 2x^2 + 3x - 2 using completing the square:
f(x) = 2x^2 + 3x - 2
First, we factor out the coefficient of x^2:
f(x) = 2(x^2 + (3/2)x) - 2
Next, we take half of the coefficint of x and square it, then add and subtract it inside the parentheses:
f(x) = 2(x^2 + (3/2)x + (3/4)^2 - (3/4)^2) - 2
Simplifying the expression inside the parentheses:
f(x) = 2[(x + 3/4)^2 - 9/16] - 2
Expanding the brackets and simplifying:
f(x) = 2(x + 3/4)^2 - 17/8
Therefore, f(x) = 2x^2 + 3x - 2 can be written in the form f(x) = 2(x + 3/4)^2 - 17/8.
Hope that helps