Question

In the function f(x)=5(x^2-4+___)+15, what number belongs in the blank to complete the square?

Answer 1

2² = 4

Explanation:

`\text{Use}\\(a-b)^2=a^2-2ab+b^2\\\\f(x)=5(x^2-4x+\underline{\ \ \ })+15\\\\x^2-4x\\\\x^2-2(x)(2)\\\\x^2-2(x)(2)+2^2=x^2-4x+4\\\\\text{Therefore}\\\\f(x)=5(x^2-4x+4)+15=5(x-2)^2+15`