Hurry plz answer the y-intercept of a parabola is 1, and its vertex is at (1,0). what function does the graph represent? a. f(x) = (x − 1)2 b. f(x) = (x + 1)2 c. f(x) = -1(x − 1)2 d. f(x) = -1(x + 1)2

Option A. The function f(x) = (x − 1)2 has a y-intercept of 1 and its vertex at (1, 0)

Explanation:

If the y-intercept represents the value of 'y' when x=0.

Let's evaluate each option:

A. f(x) = (x − 1)2  = (0 − 1)2 = 1

B. f(x) = (x + 1)2  =  (0 + 1)2 = 1

C. f(x) = -1(x − 1)2  = -1(0 − 1)2 = -1

D. f(x) = -1(x + 1)2=  -1(0 + 1)2 = -1

So only Options 'A' and 'B' has a y-intercept of 1. Options 'C' and 'D' are discarded.

Now, The vertex of a parabola is the highest or lowest point of a parabola.

The vertex form of the equation of a parabola is: y = a(x-h)2 + k, where (h, k) is the vertex point.

Then, one function with a vertex at (1, 0) should look like the following:

y = a(x-1)2.

Clearly, the option 'A' is the correct option. The function f(x) = (x − 1)2 has a y-intercept of 1 and its vertex at (1, 0)