ACT Math Algebra & Functions Mastery Hub: The Industry Found

A quadratic function $f(x)$ has a vertex at $(h, k)$ and passes through the point $(x_1, y_1)$. If the function is expressed in vertex form as $f(x) = a(x-h)^2 + k$, what is the value of 'a' that best represents the "completeness" of the quadratic's transformation from the parent function $y=x^2$?

Consider the system of equations: $y = 2x^2 - 3x + 1$ $y = 5x - 3$ If the ACT Algebra & Functions Mastery Hub emphasizes understanding the graphical interpretation of solutions, what does the solution set of this system represent geometrically?

The ACT Algebra & Functions Mastery Hub highlights the importance of function composition for advanced problem-solving. Given two functions, $f(x) = \frac{1}{x-2}$ and $g(x) = x^2 + 1$, what is the domain of the composite function $(f \circ g)(x)$?