Quadratic ManipulationIs there some easy way to transform a quadratic equation like a x 2 + b x + c into a quadratic equation of the form d ( x + s ) 2 + e ( x + s ) where a,b,c,d,e are constants and a , d , e &gt; 0-s is a root of the function

Question

Quadratic ManipulationIs there some easy way to transform a quadratic equation like   a      x    2    +  b  x  +  c into a quadratic equation of the form   d  (  x  +  s      )    2    +  e  (  x  +  s  ) where a,b,c,d,e are constants and   a  ,  d  ,  e  &amp;gt;  0-s is a root of the function

Lillianna Salazar · Accepted Answer

Step 1This is an answer to the problem OP asked before editing.let   a      x    2    +  b  x  +  c  =  d  (  x  +  s      )    2    +  e  (  x  +  s  ), compare coefficients and get the desired form  a      x    2    +  b  x  +  c  =  d  (  x  +  s      )    2    +  e  (  x  +  s  )  =  d  (      x    2    +      s    2    +  2  x  s  )  +  e  x  +  e  s which gives the equationsStep 2  a  =  d  b  =  2  s  d  +  e  c  =  d      s    2    +  e  s

Quadratic Manipulation. Is there some easy way to transform a quadratic equation like ax^2+bx+c into a quadratic equation of the form d(x+s)^2+e(x+s) where a,b,c,d,e are constants and a,d,e >= 0

Answered question

Answer & Explanation

New Questions in Algebra I