Find the direction of opening, vertex, and axis of symmetry for the quadratic function𝑦 = 3𝑥2 − 24𝑥 + 41

The given quadratic function is y = 3x² - 24x + 41.

1. Direction of Opening: The coefficient of x² in the given quadratic function is 3, which is positive. Therefore, the parabola opens upwards.

2. Vertex: The vertex of a parabola given by the equation y = ax² + bx + c is given by the point (h, k), where h = -b/2a and k = c - b²/4a. Here, a = 3, b = -24, and c = 41. So, h = -(-24)/23 = 24/6 = 4 and k = 41 - (-24)²/43 = 41 - 576/12 = 41 - 48 = -7. Therefore, the vertex of the parabola is (4, -7).

3. Axis of Symmetry: The axis of symmetry of a parabola given by the equation y = ax² + bx + c is the line x = h, where h is the x-coordinate of the vertex. So, the axis of symmetry here is the line x = 4.