Question 51·SAT Desmos Regression Practice·Advanced Math

The expressions are equivalent for every $x$. Use several inputs to find the coefficients, not to solve for $x$. Type $x_1=[1...5]$ to supply five inputs, then type $(2x_1-3)(x_1+5)-(x_1-4)^2\sim ax_1^2+bx_1+c$. The $\sim$ tells Desmos to fit the constants. Under PARAMETERS, it shows $a=1$, $b=15$, and $c=-31$. Both expressions are quadratic, so agreeing at even three distinct inputs pins down their coefficients. Here $b$ is the coefficient of $x$, meaning its multiplier, and $c$ is the constant term, with no $x$.

Type $b+2c$ on the next line. Desmos uses $b=15$ and $c=-31$ and displays $-47$. That includes both parts of the sum, not only $2c$. The value of $b+2c$ is $-47$. Choice B.