Solve (3x+30)² > 0: Finding Positive Values of a Quadratic Function

Look at the function below:

$y=\left(3x+30\right)^2$

Then determine for which values of $x$ the following is true:

$f(x) > 0$

To determine the values of $x$ for which the function $y = (3x + 30)^2$ is greater than zero, consider the following steps:

• Step 1: Recognize the structure of the function. The function is of the form $(\text{expression})^2$. For the function to be greater than zero, the expression inside the square must not equal zero.
• Step 2: Solve $3x + 30 = 0$ to find when the function equals zero.
  Subtract 30 from both sides: $3x = -30$.
  Divide by 3: $x = -10$.
• Step 3: Exclude $x = -10$ from the domain where the function is greater than 0. For all $x \neq -10$, $(3x + 30)^2$ is positive because it results from squaring a non-zero real number.

Therefore, $f(x) > 0$ for all $x \neq -10$.

The correct answer is $x\ne-10$.