Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).Consider the equation below.Use completing the square to rewrite the given equation and reveal the extreme value.The extreme value of the equation is at ( , ).Reset Next

Answer:The extreme value of the equation is (-5,-4)Step-by-step explanation:The complete question is shown in the attachment.The given equation is  [tex]y=3x^2+30x+71[/tex]Let us factor 3 out of the first two terms:[tex]y=3(x^2+10x)+71[/tex]Add and subtract the square of half the coefficient of x.[tex]y=3(x^2+10x+(5)^2)-3( 5)^2+71[/tex]We simplify (observe that the first three terms form a perfect square trinomial)[tex]y=3(x+5)^2-3*25+71[/tex][tex]y=3(x+5)^2-75+71[/tex][tex]y=3(x+5)^2-4[/tex]The extreme value of the equation is (-5,-4)