The point 2,1 is the turning point of the graph with the equation y=x^2+ax+b

a = -4, b = 3

Step-by-step explanation:

sorry, im a bit late but hoping to help others that need the answer.

when you complete the square for a quadratic, you r answer can come in the form (x+p)^2+q.

in this form, p is the opposite of the x coordinate.

and q is the same as the y coordinate.

to get p and q from this, we find the opposite of the x coordinate and use the y coordinate we are given, and plug them into this equation.

we get: (x-2)^2+1

lets complete the equation now.

(x-2)^2 = x^2 - 4x + 4, then add the one we left out = x^2 - 4x + 5.

now our equation is in the same format as y=x^2+ax+b so we can just pull out the A and B which gives us:

A = -4

B = 5

if i am wrong please feel free to correct me, ty.

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.