Question

1 identify the correct equation of the graph.
show your work here.
hint: to add an exponent (z^n), type \exponent\ or press \^a\.
o f(b)=(b - 1)^2-9
o f(b)=(b - 9)^2+1
o f(b)=(b - 9)^2-1
o f(b)=(b - 1)^2+9
o f(b)=(b + 1)^2+9
o f(b)=(b + 9)^2+1

Explanation:

Step1: Recall vertex - form of quadratic function

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

Step2: Identify the vertex from the graph

The vertex of the parabola in the graph is at the point $(1, - 9)$. So, $h = 1$ and $k=-9$.

Step3: Substitute values into vertex - form

Substituting $h = 1$ and $k=-9$ into $f(b)=a(b - h)^2+k$ (assuming $a = 1$ since the parabola opens upwards and has a standard shape), we get $f(b)=(b - 1)^2-9$.

Answer:

$f(b)=(b - 1)^2-9$