The method for completing the square can be used to write the expression
−2x^2 + 12x−5 in the form a(x + b)^2 + c, where a, b and c are constants.
Choose the option that gives the value of c.
Options
A −23 B −13
2 C 5
2 D 3 E 13 F 14
-2x^2+12x-5
-2(x^2+6x +9)-5-18
-2(x+3)^2-23
To complete the square for the expression -2x^2 + 12x - 5, follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result:
- Take half of the coefficient of x: 12/2 = 6
- Square 6: 6^2 = 36
Step 2: Add and subtract the value obtained from step 1 inside the parentheses:
- -2x^2 + 12x - 5 = -2(x^2 - 6x) - 5
- Add and subtract 36 inside the parentheses: -2(x^2 - 6x + 36 - 36) - 5
- Rearranging: -2((x^2 - 6x + 36) - 36) - 5
- Simplifying the expression inside the parentheses: -2(x - 6)^2 + 2(36) - 5
- Combining like terms: -2(x - 6)^2 + 72 - 5 = -2(x - 6)^2 + 67
Now, the expression is in the form a(x + b)^2 + c, where a = -2, b = -6, and c = 67.
Therefore, the correct option from the given choices is:
C) 5