The function that the graph represents is f(x) = (x-1)^2 + 1.

Here's the step-by-step explanation:

1. The vertex form of a parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

2. Given that the vertex is at (1,0), we can substitute h = 1 and k = 0 into the vertex form, giving us f(x) = a(x-1)^2.

3. The y-intercept of a graph is the point where the graph crosses the y-axis. This happens when x = 0. Given that the y-intercept is 1, we can set x = 0 in our function and solve for a: 1 = a(0-1)^2 = a, so a = 1.

4. Substituting a = 1 back into our function gives us the final function: f(x) = (x-1)^2 + 1.

Question

The function that the graph represents is f(x) = (x-1)^2 + 1.

Here's the step-by-step explanation:

1. The vertex form of a parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

2. Given that the vertex is at (1,0), we can substitute h = 1 and k = 0 into the vertex form, giving us f(x) = a(x-1)^2.

3. The y-intercept of a graph is the point where the graph crosses the y-axis. This happens when x = 0. Given that the y-intercept is 1, we can set x = 0 in our function and solve for a: 1 = a(0-1)^2 = a, so a = 1.

4. Substituting a = 1 back into our function gives us the final function: f(x) = (x-1)^2 + 1.

Knowee AI · Accepted Answer

The function that the graph represents is f(x) = (x-1)^2 + 1.

Here's the step-by-step explanation:

1. The vertex form of a parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

2. Given that the vertex is at (1,0), we can substitute h = 1 and k = 0 into the vertex form, giving us f(x) = a(x-1)^2.

3. The y-intercept of a graph is the point where the graph crosses the y-axis. This happens when x = 0. Given that the y-intercept is 1, we can set x = 0 in our function and solve for a: 1 = a(0-1)^2 = a, so a = 1.

4. Substituting a = 1 back into our function gives us the final function: f(x) = (x-1)^2 + 1.

Select the correct answer.The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?

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