The analysis of the equations indicates that we get;
Part A; (c) y = 4·(x - 3)²
Part B; (A) Minimum
Part C; (3, 0)
The steps used to obtain the correct equation, and the minimum point are as follows;
Part A
The maximum or minimum of a function is the vertex of the function.
The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k
Where; (h, k) represents the coordinates of the vertex of the quadratic equation
a represents the stretch of the function and the reflection across x-axis
Comparing the specified equations, the equation that best approximates the vertex for of the quadratic equation is the option (c) y = 4·(x - 3)²
Therefore, the equation that reveals the maximum or minimum is the option (c) y = 4·(x - 3)²
Part B;
The value in the equation y = 4·(x - 3)² corresponding to the value a in the vertex form of the equation of a quadratic equation f(x) = a·(x - h)² + k is a = 4, which indicates that the leading coefficient of the equation is positive, corresponding to a parabola that opens up, having a minimum point; Therefore, the equation has a minimum
Part C;
The coordinates of the minimum point of the equation y = 4·(x - 3)², obtained by comparing the equation to the vertex form of a quadratic equation f(x) = a·(x - h)² + k, with a vertex of (h, k), where h = 3, and k = 0 is (h, k) = (3, 0)
The vertex is (3, 0)