Question

Find a quadratic function associated with vertex (h, k) = (2, 1) and point (x, y) = (6, 7) that the parabola passes through.

Answer 1

Try this option:
1. for vertex (2;1) the first equation is: h=-b/2a, it means 2=-b/2a or b=-4a;
2. for vertex (2;1) the second equation is: ax²+bx+c=y, it means 1=4a+2b+c;
3. for point (6;7) the third equation is: ax²+bx+c=y, it means 7=36a+6b+c.
4. using three equation, it is possible to make up the system of equations (and solve it). Details are in the attached picture.
answer:
$y= \frac{3}{8}x^2 - \frac{3}{2}x + \frac{5}{2}$
The graph is in the attachment.