Question

The point (2,1) is the turning point of y=x^2+ax+b where a and b are integers.Find the values of a and b

Answer 1

In any parabola, the vertex is the turning point. And the x-coordinate of the vertex can be found using

$x_V=-\dfrac{b}{2a}$

So, in your case, you have

$2=-\dfrac{a}{2}\iff a=-4$

So, your equation actually looks like

$y=x^2-4x+b$

Now impose the passing through (2,1), i.e. substitute x=2, y=1 and solve for b:

$1=4-8+b \iff b=5$