Writing Equations of Quadratics

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

The axis of symmetry can be found using the formula: Axis of Symmetry = $$\frac{{x_1 + x_2}}{2}$$ , where $$x_1$$ and $$x_2$$ are the zeros of the function.

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

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

The 'a' value indicates the direction of the parabola (upward if positive, downward if negative) and its width (larger absolute value means narrower).

Use the vertex form $$y = a(x - 3)^2 - 7$$ and solve for 'a' using the point (1, -10).

If a quadratic function has zeros at $$x = p$$ and $$x = q$$ , it can be factored as $$y = a(x - p)(x - q)$$ .

If the coefficient 'a' in the vertex form $$y = a(x - h)^2 + k$$ is positive, the parabola opens upwards; if negative, it opens downwards.

The y-coordinate of the vertex can be found using the formula $$k = c - \frac{b^2}{4a}$$ from the standard form $$y = ax^2 + bx + c$$ .

The x-coordinate of the vertex can be found using the formula $$h = -\frac{b}{2a}$$ from the standard form $$y = ax^2 + bx + c$$ .