To express the quadratic expression 2x^2 - 6x + 5 in the form a(x - b)^2 + c, we need to complete the square. Here's how you can do it step by step:
1. Start with the given quadratic expression: 2x^2 - 6x + 5
2. To complete the square, first factor out the coefficient of x^2, which is 2:
2(x^2 - 3x) + 5
3. To complete the square within the parentheses, take half of the coefficient of x (-3 in this case), square it, and add/subtract it inside the parentheses:
2(x^2 - 3x + (-3/2)^2 - (-3/2)^2) + 5
2(x^2 - 3x + 9/4 - 9/4) + 5
2(x - 3/2)^2 - 9/2 + 5
2(x - 3/2)^2 - 9/2 + 10/2
2(x - 3/2)^2 + 1/2
Therefore, the quadratic expression 2x^2 - 6x + 5 can be expressed in the form a(x - b)^2 + c as:
a = 2
b = 3/2
c = 1/2
So, the values of a, b, and c are:
a = 2
b = 3/2
c = 1/2
