Question 215713
{{{y = -x^2 + 2x + 3}}}


Step 1.  Let's factor out negative 1 so now we have {{{y=-1(x^2-2x-3)}}}


Step 2.  We need two integers m and n such that their sum is -2=m+n and their product mn=-3.


Step 3.  The integers are -3 and 1.  Then, {{{x^2-3x-3=(x-3)(x+1)}}}


Step 4.  ANSWER:  y = -x^2 + 2x + 3=-1*(x-3)(x+1) when y=0 we are finding x as solutions where it intersects the x-axis or in our case (x-3)=0 and (x+1)=0 or x=3 and x=-1.


You can also use the quadratic formula given as {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=-1, b=2 and c=3.


The graph is shown below:


*[invoke quadratic "x", -1, 2, 3 ]


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J