Question

7.
equation in vertex form: y=(x-\square)^2\square
equation in factored form: y=\square

Explanation:

Step1: Find vertex coordinates

The vertex of the parabola is at (5, -1) (lowest point on the graph).

Step2: Fill vertex form constants

Vertex form is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex. Here $h=5$, $k=-1$, and $a=1$ (since it opens upward with standard width). So $y=(x-5)^2-1$.

Step3: Find x-intercepts for factored form

From the graph, x-intercepts are at $x=4$ and $x=6$. Factored form is $y=a(x-r)(x-s)$, so $y=(x-4)(x-6)$.

Answer:

Vertex form: $y=(x-5)^2-1$
Factored form: $y=(x-4)(x-6)$

(Boxed values: first box 5, second box -1; factored form box $(x-4)(x-6)$)