Graphing Quadratics in Vertex Form

The vertex form of a quadratic equation is given by $$y = a(x - h)^2 + k$$ , 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 domain of a quadratic function is all real numbers, represented as @@(- ext{∞}, ext{∞})@@.

If a > 0, the range of the quadratic function is $$[k, \text{∞})$$ , where (h, k) is the vertex.

If a < 0, the range of the quadratic function is $$(-\text{∞}, k]$$ , where (h, k) is the vertex.

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

The y-intercept is (0, 22).

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

The x-intercepts are (-5, 0) and (-3, 0).

The 'a' value indicates the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.