The parabola vertex formula serves as the operational engine for this quiz. When Edgenuity supplies an equation such as $f(x) = -2x^2 + 12x - 10$, you must extract the turning point in two clear steps.
First, identify $a = -2$ and $b = 12$. Substitute these into the axis of symmetry formula:
$$x = -\frac{12}{2(-2)} = -\frac{12}{-4} = 3$$
This single calculation yields two answers simultaneously. The axis of symmetry is the line $x = 3$. The horizontal coordinate of the vertex is also $3$.
Second, calculate the vertical coordinate by plugging $x = 3$ back into the original function:
$$f(3) = -2(3)^2 + 12(3) - 10$$
$$f(3) = -2(9) + 36 - 10$$
$$f(3) = -18 + 36 - 10 = 8$$
The vertex rests at $(3, 8)$. Because the leading coefficient is negative ($a = -2$), the parabola curves downward. This makes the vertex the highest point on the curve, establishing a maximum value of 8. If the question asks where the maximum occurs, the answer is at $x = 3$. If it asks for the maximum value itself, the answer is $8$. Edgenuity tests this exact distinction repeatedly to catch inattentive students.
