Question 1074571

Determine the quadratic function f whose graph has the following,
The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,
<pre>{{{f(x) = a(x - h)^2 + k}}} ------- Quadratic function, in vertex-form 
{{{1 = a(3 - 2)^2 + - 1}}} ------ Substituting (2, - 1) for (h, k), and (3, 1) for [x, f(x)]
1 = a - 1
1 + 1 = a
2 = a
{{{f(x) = 2(x - 2)^2 - 1}}} 
{{{f(x) = 2(x^2 - 4x + 4) - 1}}} 
{{{f(x) = 2x^2 - 8x + 8 - 1}}} 
Quadratic function: {{{highlight_green(matrix(1,3, f(x), "=", 2x^2 - 8x + 7))}}}