Rewrite the following quadratic function in standard (vertex) form. Report numbers as fractions when applicable. f(x)=3x2+5x−7

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Rewrite the following quadratic function in standard (vertex) form. Report numbers as fractions when applicable.  f(x)=3x2+5x−7

Anthony Caraballo · Accepted Answer

Step 1  Given quadratic function is as below:  f(x)=3x2+5x−7  Step 2  A standard vertex form is in the form shown below.  f(x)=a(x−b)2+c  In order to rewrite into the standard (vertex) form you have to do complete the square first.   Step 3   To complete the square, follow the below steps:  f(x)=3x2+5x−7  Take 3 common from 1st and 2nd term  f(x)=3(x2+53x)−7  Rewrite the 2nd term  f(x)=3(x2+256x)−7  Add and subtract (56)2 from inside the bracket  f(x)=3(x2+256x+(56)2−(56)2)−7  Complete the square using: a2+2ab+b2=(a+b)2  f(x)=3((x+56)2−(56)2)−7  Step 4  Simplify  f(x)=3(x+56)2−3(56)2−7  f(x)=3(x+56)2−32536−7  f(x)=3(x+56)2−2512−7  f(x)=3(x+56)2−10912

Rewrite the following quadratic function in standard (vertex) form. Re

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