Question 1196172
A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b
<pre>I hope for your sanity that you didn't pay any attention to that woman's method of solving this porblem. She has this habit
of solving a variable in terms of another variable in fractional form, which is TOTALLY UNNECESSARY and LUDICROUS!! 

g(-2) = 6 signifies that x = - 2 when y = 6. We then have: 
   {{{matrix(1,3, g(x), "=", ax^2 + bx + 2)}}}
 {{{matrix(1,3, g(- 2), "=", a(- 2)^2 + b(- 2) + 2)}}} ---- Substituting - 2 for x
g(- 2) = 4a - 2b + 2
     6 = 4a - 2b + 2 ----- Substituting 6 for y, or g(- 2)  
     4 = 4a - 2b____2(2) = 2(2a - b)_____2 = 2a - b ----- eq (i)

Likewise,  g(3) = 11 signifies that x = 3 when y = 11. We then have: 
 {{{matrix(1,3, g(x), "=", ax^2 + bx + 2)}}}
 {{{matrix(1,3, g(3), "=", a(3)^2 + b(3) + 2)}}} ----- Substituting 3 for x
 g(3) = 9a + 3b + 2
   11 = 9a + 3b + 2 ----- Substituting 11 for y, or g(3)  
    9 = 9a + 3b____3(3) = 3(3a + b)_____3 = 3a + b ----- eq (ii)

We then have:
2 = 2a - b ----- eq (i)
3 = 3a + b ----- eq (ii
5 = 5a ---- Adding eqs (i) & (ii)
{{{highlight_green(matrix(1,5, highlight(a), "=", 5/5, "=", highlight(1)))}}}

3 = 3(1) + b ------ Substituting 1 for a in eq (ii)
{{{highlight_green(matrix(1,5, highlight(b), "=", 3 - 3, "=", highlight(0)))}}}</pre>