After you substitute $x=2$ into $-3x^2+12x+5$, make sure to do exponents first, then multiplication, then addition.

When you evaluate $-3x^2$ at $x=2$, square the 2 first to get $2^2$, then multiply by $-3$. Do not square the $-3$.

In a Desmos expression line, type -3*(2)^2 + 12*(2) + 5 and press Enter. The value that Desmos outputs is the value of $g(2)$.

The notation $g(2)$ means: take the formula for $g(x)$ and replace every $x$ with $2$, then simplify.

Start with the function:

Now substitute $x=2$:

Next, handle the exponent first.

Compute $2^2$ and then multiply:

• $2^2 = 4$
• So $-3(2)^2 = -3(4) = -12$
• And $12(2) = 24$

Now $g(2)$ becomes:

Combine the numbers step by step:

• $-12 + 24 = 12$
• $12 + 5 = 17$

So $g(2) = 17$, which corresponds to choice C.