Answer:
Explanation:
To express the quadratic expression x^2 - 8x + 5 in the form (x - a)^2 - b, we need to complete the square.
Step 1: Take half of the coefficient of x and square it. In this case, half of -8 is -4, and (-4)^2 is 16.
Step 2: Add and subtract the value obtained in Step 1 inside the parentheses of the quadratic expression. This maintains the equality of the expression, as we are adding and subtracting the same value.
So, x^2 - 8x + 5 can be written as:
x^2 - 8x + 16 - 16 + 5
Step 3: Group the first three terms and write them as a perfect square binomial.
(x^2 - 8x + 16) - 16 + 5
(x - 4)^2 - 16 + 5
Step 4: Simplify the expression inside the parentheses and combine like terms.
(x - 4)^2 - 11
Therefore, the expression x^2 - 8x + 5 can be written in the form (x - a)^2 - b as (x - 4)^2 - 11, where a = 4 and b = 11.