select the correct answer.\nthe y - intercept of a parabola is 1, and its vertex is at (1,0). what function…

select the correct answer.\nthe y - intercept of a parabola is 1, and its vertex is at (1,0). what function does the graph represent?\na. (f(x)=(x - 1)^2)\nb. (f(x)=(x + 1)^2)\nc. (f(x)=-1(x - 1)^2)\nd. (f(x)=-1(x + 1)^2)

select the correct answer.\nthe y - intercept of a parabola is 1, and its vertex is at (1,0). what function does the graph represent?\na. (f(x)=(x - 1)^2)\nb. (f(x)=(x + 1)^2)\nc. (f(x)=-1(x - 1)^2)\nd. (f(x)=-1(x + 1)^2)

Answer

Explanation:

Step1: Recall vertex - form of parabola

The vertex - form of a parabola is $f(x)=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. Given the vertex is $(1,0)$, so $h = 1$ and $k = 0$, and the function is $f(x)=a(x - 1)^2$.

Step2: Use the y - intercept

The y - intercept is the value of the function when $x = 0$. We know that when $x = 0$, $y=f(0)=1$. Substitute $x = 0$ into $f(x)=a(x - 1)^2$: $f(0)=a(0 - 1)^2$. Since $f(0)=1$, we have $a(0 - 1)^2=1$, which simplifies to $a\times1 = 1$, so $a = 1$.

Answer:

A. $f(x)=(x - 1)^2$