In the function f(x) = 5(x2 − 4x + ____) + 15, what number belongs in the blank to complete the square
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Given the function:
f(x) = 5(x^2 - 4x + __ ) + 15
Complete the square.
Solution:
In order to complete the square, we must first equate the function f(x) to 0. After equating, we divide the numerical coefficient of the 2nd value inside the parenthesis which is -4 by 2, and the we square the quotient. That squared quotient will become the missing term to be added.
= -4/2
= 2
= 2^2
= 4
Add 4 to both sides of the equation.
5(x^2 - 4x + 4) + 15 = 4
Transpose 4 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
5(x - 2)^2 + 15 - 4 = 0
5(x - 2)^2 + 11 = 0
Final answer:
5(x - 2)^2 + 11 = 0