Matching Graphs, Tables & Equations

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where a, b, and c are constants and a ≠ 0.

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

The vertex of the parabola given by $$y = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ .

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

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation $$x = -\frac{b}{2a}$$ .

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

A linear equation is an equation of the first degree, which can be written in the form $$y = mx + b$$ , where m is the slope and b is the y-intercept.

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated as $$m = \frac{y2 - y1}{x2 - x1}$$ .