Question

Rewrite the function by completing the square. f(x)=x^2+16x-46
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Answer 1

`f(x)=(x+8)^(2)-110`

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`