Answer:
C
Step-by-step explanation:
When completing the square, we essentially want to create a perfect square trinomial by adding a constant.
If we have the following expression:
[tex]x^2+bx[/tex]
And we want to complete the square, we will need to divide the b-coefficient by half and then square it.
Thus, the added term should be:
[tex](b/2)^2[/tex]
In the given equation, we have:
[tex](x^2-8x)-10[/tex]
The b term here is 8. Therefore:
[tex](8/2)^2\\=(4)^2\\=16[/tex]
The value we would add would be 16.
The answer is C.
Further notes:
To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:
[tex](x^2-8x)-10\\=(x^2-8x+16)-10-16\\[/tex]
The expression inside the parentheses is now a perfect square trinomial. Factor it:
[tex]=((x)^2-2(4)(x)+(4)^2)-26\\=(x-4)^2-26[/tex]
And we are done!
A quadratic function equation is as follows:
[tex]ax^{2} + bx + c[/tex]
To complete the square, move the constant (c) to the other side of the equation and take half of the b value, square it, and add and subtract the same number.
In this problem, you will add 16.
[tex] \frac{ - 8}{2} = - 4[/tex]
[tex] - 4^{2} = 16[/tex]
