Question

What does the equation y = x2 - 6x + 5 become after completing the square?

Answer 1

Hello!

The answer is:

The answer is: C.

$y=(x-3)^{2}-4$

Why?

To answer this question, we need to remember the completing square process.

We can complete the square in the following way:

- Make the function equal to 0.

- Isolate the constant number (c).

- Find the number that completes the square using the following formula:

$(\frac{b}{2})^{2}$

- Add the number that completes the square to both sides of the equation.

- Factorize the trinomial on one of the sides of the equation, and simplify the other side.

So, We are given the equation:

$y=x^{2} -6x+5$

- Making it equal to 0, we have:

$0=x^{2} -6x+5$

- Isolating the constant, we have:

$x^{2} -6x=-5$

- Finding the number that completes the square:

$(\frac{b}{2})^{2}=(\frac{-6}{2})^{2}=(-3)^{2}=9$

- Adding it to both sides of the equation:

$x^{2} -6x+9=-5+9$

- Factoring and simplifying, we have:

$x^{2} -6x+9=-5+9$

We need to find two numbers which product gives as result "9" and its algebraic sum gives as result "-6", this numbers is "-3", then, factoring, we have:

$(x-3)^{2}=4$

$(x-3)^{2}-4=0$

Then, the equation after completing the square will be:

$y=(x-3)^{2}-4$

Hence, the answer is:

C. $y=(x-3)^{2}-4$

Have a nice day!

Answer 2

Answer: Option B

Step-by-step explanation:

Given the quadratic equation $y=x^2-6x+5$:

You know that:

$(\frac{b}{2})^2=(\frac{6}{2})^2=3^2$

Group the variable "x" inside a parentheses:

$y=(x^2-6x)+$

Then, now you need to add 3² inside the parentheses  and subtract 3² outside of the parentheses. Thenrefore, rewriting, you get:

$y=(x^2-6x+3^2)+(5-3^2)\\y=(x-3)^2-4$

This matches with the option B.