Question

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

Answer 1

f(x) = (x − 1)2

Explanation:

Answer 2

Equation of function, y = (x-1)²

Explanation:

The general formula of a parabola symmetric about x - axis is given by (x-h)²=4a(y-k), where (h,k) is the vertex.

Here (h, k) = (1,0)

So, we have (x-1)²=4a(y-0)

(x-1)²=4ay

One point on the parabola is (0,1) since y intercept is 1.

Substituting

(0-1)²=4 x a x 1

1 = 4 a

`a=(1)/(4)`

Equation of parabola,

`(x-1)^2=4*(1)/(4) *y\\ \\ (x-1)^2=y\\ \\ y=(x-1)^2`

Equation of function, y = (x-1)²