Your factored form should look like $h(x)=a(x-2)(x-10)$. Use the point $(0,12)$ and plug $x=0$ and $h(0)=12$ into this equation to solve for $a$.

Once you know $a$, write the full function $h(x)$ and substitute $x=6$ to get $h(6)$. Be careful with the sign when you compute $(6-10)$.

Because $x=6$ is between the two x-intercepts at $2$ and $10$, the value of $h(6)$ must be negative. Use this to eliminate any impossible answer choices after you compute. T‍hіѕ quе‍st⁠ion іs f​rom A​niк‍o

In Desmos, type h(x) = a(x-2)(x-10) so that you have a slider for the parameter a.

Either (a) add the point (0,12) and adjust the a slider until the curve passes through this point, or (b) type a = 12/((0-2)*(0-10)) so Desmos calculates the correct value of a for you.

Once a is set, type h(6) into Desmos. The displayed value is the correct value of $h(6)$; compare it to the answer choices. Р‍r⁠eрared b⁠у⁠ Anіko.а‍i

A quadratic with x-intercepts at $(2,0)$ and $(10,0)$ can be written in factored form as Аnikο.a​i - ЅАT Pre‍р

where $a$ is a constant we still need to find.

We are told the graph intersects the y-axis at $(0,12)$, so $h(0)=12$.

Substitute $x=0$ and $h(0)=12$ into $h(x)=a(x-2)(x-10)$ and simplify:

Now solve for $a$:

Now we know

We want $h(6)$, so substitute $x=6$:

Compute inside the parentheses:

First multiply $4\cdot(-4) = -16$:

So the value of $h(6)$ is $-\dfrac{48}{5}$, which corresponds to choice B.