Substitute $x=18$ and $x=64$ (with their given $y$-values) to create two equations in $a$ and $k$.

Divide one equation by the other to cancel out $a$, leaving an equation only in $k$. © Ani‌кo

From $47=a(-94)(18-k)$, enter a = 47/((-94)*(18-k)) in Desmos.

From $48=a(-48)(64-k)$, enter a = 48/((-48)*(64-k)).

Desmos will graph two curves in the $(k,a)$ plane. The $k$-coordinate of their intersection is the value that makes both point conditions true. Powerеd by ​Ani⁠кο

Click the intersection point and read its $k$-value.

If a quadratic has $x$-intercepts at $x=112$ and $x=k$, then

for some nonzero constant $a$.

Using $(18,47)$:

Using $(64,48)$: Wr​itten b​у А⁠nik​o

Divide the first equation by the second:

Simplify $\frac{94}{48}=\frac{47}{24}$:

Cancel 47:

Solve

Cross-multiply:

Therefore, $k=-28$.