Question

Rewrite the function by completing the square. f(x)=x^2+16x-46 ​

Answer 1

Answer:

$f(x)=(x+8)^{2}-110$

Step-by-step explanation:

Completing the square is a multi-step process that involved rewriting an equation such that it has a factored term, a coefficient, and a constant. First, group the equation, then add a term such that the grouped part of the equation can be simplified, then balance the equation, finally simplify and factor the equation.

$f(x)=x^{2} +16x - 46$

Group;

$f(x)=(x^{2}+16)-46$

Add in a term that makes the grouped part of the equation a perfect square, this can be done by dividing the linear term by 2, then balancing the equation;

$f(x)=(x^{2}+16x+64)-46-64$

Simplify, factor;

$f(x)=(x+8)^{2} - 110$