Question 1060914
What is the equation of the parabola passing through the points A(1,1) , B(2,2) , C(-1,5) and axis parallel to the y-axis
<pre>Standard form equation of a vertical parabola: {{{matrix(1,5, f(x) = ax^2 + bx + c, "=====>", y = ax^2 + bx + c, "=====>", ax^2 + bx + c = y)}}} 

A (1, 1)
{{{a(1)^2 + b(1) + c = 1}}} ------ Substituting A (1, 1)
a + b + c = 1 --------- eq (i)

B (2, 2)
{{{a(2)^2 + b(2) + c = 2}}} ------ Substituting B (2, 2)
4a + 2b + c = 2 ------- eq (ii)

C (- 1, 5)
{{{a(- 1)^2 + b(- 1) + c = 5}}} --- Substituting C (- 1, 5)
a - b + c = 5 --------- eq (iii)

2b = - 4 ------- Subtracting eq (iii) from eq (i)
{{{highlight(matrix(1,5, b, "=", (- 4)/2, or, - 2))}}}

a - 2 + c = 1 ------ Substituting - 2 for b in eq (i) 
a + c = 3 ---------- eq (iv)

4a - 4 + c = 2 ----- Substituting - 2 for b in eq (ii)  
4a + c = 6 --------- eq (v)
3a = 3 ------------- Subtracting eq (iv) from eq (v)
{{{highlight(matrix(1,5, a, "=", 3/3, or, 1))}}}

1 - 2 + c = 1 ------ Substituting 1 for a, and - 2 for b in eq (i)
- 1 + c = 1
{{{highlight(matrix(1,5, c,"=", 1 + 1, or, 2))}}}

{{{y = ax^2 + bx + c}}} 
{{{highlight_green(y = x^2 - 2x + 2)}}} ----- Substituting 1 for a, - 2 for b, and 2 for c</pre>