Question 55·SAT Desmos Regression Practice·Advanced Math

The equality holds for every $x$, so you can give Desmos inputs $1$ through $5$. Type $x_1=[1...5]$, then type the given equality with every $x$ changed to $x_1$ and $=$ changed to $\sim$. This regression fits $p$ and $q$ rather than graphing $x$. Under PARAMETERS, Desmos reports approximately $(p,q)=(17.775,0.1125)$.

Keep those lines and type $(p-2q)^2$ beneath them. Desmos uses its fitted constants and displays $308$. The fitted pair gives the square, so you don't need to find $p-2q$ first. The requested value is $308$. Choice B.

Because the identity holds for every input, set $x=0$. Every term containing $x$ vanishes, leaving the product $pq$:

Multiply the constants:

Subtract $15$:

Set $x=1$ for a second condition. The right side is $11+17=28$, and your known $pq$ will leave $p+2q$. Substitute $1$:

Distribute:

Replace $pq$ with $2$:

Subtract $10$:

You know the sum $p+2q$ and the product $pq$. Use $(a-b)^2=(a+b)^2-4ab$ with $a=p$ and $b=2q$:

Insert the values:

The sum and product give the square without finding $p$ and $q$ separately. Type $18^2-8(2)$ in Desmos; it displays $308$. The requested value is $308$. Choice B.