Answer Happy

Quadratic Spline.
Show how to obtain the constants below (a1,b1,c1 etc...) from the
equations above through algebra particularly substitution or
elimination. Please show complete solution and and also neat
handwriting.
eqn 1 Condition #1: From the Interior knots: Q, R at point Q: (4)2 + b(4) + C1 = 2 az(4)2 + b (4) + C2 = 2 at point R: az(7)2 + b2(7) + C2 = 8 egn 3 az(7)2 + b3(7) + C3 = 8 egn 2 ------- eqn 4 eqn 5 Condition #2: From the exterior knots: P, S At point P: a(3)+ b (3) + C1 = 5 At point S: a3(92 + b3(9) + c3 = 6 Condition #3: First derivatives of the interior knots are equal 2a,x + b = 2a2x + b2 ----- eqn 7 2a2x + b2 = 2a3x + bg eqn 8 egn 6 Condition #4: a, = 0 eqn 9 From the 9 equations, by solving for the unknowns algebraically, we will get the following: a1 = 0 a2 = 15/9 a3 = -4 b1 = -3 b2 = -49/3 b3 = 63 c1 = 14 c2 = 122/3 c3 = -237