Question

Choose an expression equivalent to 2x2-12x+23

Group of answer choices

2(x+23)2-1

2(x+3)2+14

2(x-3)2+5

2(x-3)2+13

Answer 1

Answer: 2(x-3)2+13

To find the equivalent expression, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers. This property is given by the following equation:

(a-b)2 = a2-2ab+b2

In this case, the expression we are trying to simplify is 2x2-12x+23, which we can rewrite using the property of square roots as follows:

2x2-12x+23 = 2(x2-6x+11)

Then, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers to simplify the expression as follows:

2x2-12x+23 = 2(x2-6x+11) = 2(x2-6x+36-25)

Finally, we can use the commutative property of addition and the associative property of addition to simplify the expression even further:

2x2-12x+23 = 2(x2-6x+36-25) = 2((x-3)2+11) = 2(x-3)2+22

Therefore, the equivalent expression to 2x2-12x+23 is 2(x-3)2+13. This means that the correct answer is 2(x-3)2+13.