Introduction to Quadratics Lesson 1

A quadratic function is a polynomial function of degree 2, typically in the form of $$y = ax^2 + bx + c$$ , where a, b, and c are constants and a ≠ 0.

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ .

The graph of a quadratic function is a parabola, which can open upwards or downwards.

The direction of a parabola is determined by the coefficient 'a' in the quadratic function. If 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ to find the x-coordinate, and then substituting it back into the function to find the y-coordinate.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation $$x = -\frac{b}{2a}$$ .

The roots of a quadratic equation are the values of x for which the quadratic function equals zero, also known as the x-intercepts.

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

The roots can be found using the quadratic formula: $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ .