Find the direction of opening, vertex, and axis of symmetry for the quadratic function𝑦 = −5 − 6𝑥 − 2𝑥2

The quadratic function given is y = -5 - 6x - 2x^2.

First, let's rewrite this in the standard form of a quadratic function, which is y = ax^2 + bx + c. So, our function becomes y = -2x^2 - 6x - 5.

1. Direction of Opening: The coefficient of x^2 (a) is -2, which is less than 0. Therefore, the parabola opens downwards.

2. Vertex: The vertex of a parabola given in the form y = ax^2 + bx + c is given by the point (h, k), where h = -b/2a and k = c - b^2/4a. Substituting the given values, h = -(-6)/(2*-2) = 1.5 and k = -5 - (-6)^2/(4*-2) = -4. Therefore, the vertex of the parabola is (1.5, -4).

3. Axis of Symmetry: The axis of symmetry of a parabola is the vertical line x = h, where h is the x-coordinate of the vertex. Therefore, the axis of symmetry of this parabola is x = 1.5.