Question

consider the following relation.

\\(3x^2 + 2x = -2x + 4y\\)

step 2 of 3 : evaluate the function found in the previous step at \\(x = -2\\).

answer

\\(f(-2) = \square\\)

Explanation:

Step1: Isolate $y$ to get function

Rearrange the given equation to solve for $y$:

$$\begin{align*} 3x^2 + 2x &= -2x + 4y\\ 3x^2 + 2x + 2x &= 4y\\ 3x^2 + 4x &= 4y\\ y &= \frac{3x^2 + 4x}{4}\\ f(x) &= \frac{3}{4}x^2 + x \end{align*}$$

Step2: Substitute $x=-2$ into function

Plug $x=-2$ into $f(x)$:

$$\begin{align*} f(-2) &= \frac{3}{4}(-2)^2 + (-2)\\ &= \frac{3}{4}(4) - 2\\ &= 3 - 2 \end{align*}$$

Answer:

$1$