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

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Answer:

[tex]f(x)=(x+8)^{2}-110[/tex]

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.

[tex]f(x)=x^{2} +16x - 46\\[/tex]

Group;

[tex]f(x)=(x^{2}+16)-46[/tex]

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;

[tex]f(x)=(x^{2}+16x+64)-46-64[/tex]

Simplify, factor;

[tex]f(x)=(x+8)^{2} - 110[/tex]

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