Question

Determine the quadratic function whose vertex is at -1,1 and the y-intercept is 0,2

Answer 1

To determine the quadratic function, we can use the vertex form and substitute the given values. The quadratic function is f(x) = (x+1)^2 + 1.

Step-by-step explanation:

To determine the quadratic function, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k, where (h, k) is the vertex.

Given that the vertex is (-1, 1), we have f(x) = a(x+1)^2 + 1.

Since the y-intercept is (0, 2), we can substitute these coordinates into the equation: 2 = a(0+1)^2 + 1.

Solving for a, we get a = 1.

Therefore, the quadratic function with the given vertex and y-intercept is f(x) = (x+1)^2 + 1.