Quadratic Function - Vertex Form

The vertex form of a quadratic function is given by the equation: $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

To find the vertex of a parabola in vertex form $$y = a(x - h)^2 + k$$ , identify the values of h and k. The vertex is (h, k).

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

To find the y-intercept, set x = 0 in the vertex form equation and solve for y.

The range of a quadratic function $$y = a(x - h)^2 + k$$ depends on the value of 'a'. If 'a' > 0, the range is [k, ∞); if 'a' < 0, the range is (-∞, k].

Check the value of 'a' in the vertex form $$y = a(x - h)^2 + k$$ . If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, use the method of completing the square.

The vertex of the parabola is (-5, -4).

To find the x-intercepts, set y = 0 in the quadratic equation and solve for x.

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation $$x = h$$ , where (h, k) is the vertex.