Question

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

Answer 1

The point 2,1 is the turning point of the graph with the equation y=x^2+ax+b is the vertex of the parabola. To find the vertex, we need to find the x-coordinate and y-coordinate of the vertex. The x-coordinate is -a/2 and the y-coordinate is obtained by substituting the x-coordinate into the equation.

Step-by-step explanation:

The given equation is a quadratic equation in the form y = x^2 + ax + b. The turning point of the graph is the vertex of the parabola.

To find the turning point, we first need to find the x-coordinate of the vertex. The x-coordinate of the vertex is given by -a/2, where a is the coefficient of x in the equation.

Substituting the value of a = 1, we have x = -1/2. To find the y-coordinate of the vertex, substitute this value of x into the equation. We get y = (-1/2)^2 + a(-1/2) + b = 1/4 - a/2 + b.

Answer 2

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.