2.1 Key Features & Vertex Form of Quadratics

The standard form of a quadratic equation is given by $$y = ax^2 + bx + c$$ , where a, b, and c are constants.

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.

In the vertex form $$y = a(x - h)^2 + k$$ , the vertex is the point (h, k).

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation $$x = h$$ in vertex form.

The range is from the vertex's y-coordinate to infinity, expressed as $$[k, \, \text{infinity})$$ if the vertex is (h, k).

The range is from negative infinity to the vertex's y-coordinate, expressed as $$(-\text{infinity}, k]$$ if the vertex is (h, k).

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x.

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.

If the vertex is at its minimum, the parabola opens upwards, and the vertex is the lowest point on the graph.