Question

given the quadratic function y=x^2+ax+b, the minimum value is -3, and the graph passes through point (1,1). find the values of the consists a and b.​

Answer 1

To find the values of a and b in the quadratic equation y = x^2 + ax + b, we need two pieces of information. Here, the minimum value is -3 and the graph passes through (1,1).

We can use these two pieces of information to write two equations:

y = x^2 + ax + b must equal -3 when x = 0 (to find the minimum value)
y = x^2 + ax + b must equal 1 when x = 1 (to find the point that the graph passes through)
Using these two equations, we can solve for a and b:

-3 = 0^2 + a * 0 + b
b = -3
1 = 1^2 + a * 1 + (-3)
a = 1
So the values of a and b are a = 1 and b = -3