Question 1162223
<pre>
The minimum point of a quadratic formula is the vertex.

{{{y = Ax^2 + Bx + C}}}

Use vertex formula:

{{{-B/(2A) = 7}}}
{{{-B=14A}}}
{{{B=-14A}}}

Substitute in

{{{y = Ax^2 + Bx + C}}}
{{{y = Ax^2 + (-14A)x + C}}}
{{{y = Ax^2-14Ax+C}}}

Substitute (x,y) = (7,-3)

{{{-3 = A(7)^2-14A(7)+C}}}

{{{-3 = 49A-98A+C}}}

{{{-3 = -49A+C}}}

Substitute (x,y) = (9,9)

{{{9 = A(9)^2-14A(9)+C}}}

{{{9 = 81A-126A+C}}}

{{{9 = -45A+C}}}

{{{system(-3 = -49A+C,9 = -45A+C)}}}

Multiply the first equation by -1

{{{system(3 = 49A-C,9 = -45A+C)}}} 

Add the two equations term by term:

{{{12=4A}}}

{{{3=A}}}

{{{B=-14A}}}

{{{B=-14(3)}}}

{{{B=-42}}}

{{{3 = 49A-C}}}
{{{3 = 49(3)-C}}}
{{{3 = 147-C}}}
{{{C=144}}}


{{{y = Ax^2 + Bx + C}}}
{{{y = 3x^2 - 42x+144}}}

Edwin</pre>