In the above, the red variables are what we call parameters. They represent fixed quantities, rather than changing ones (like the independent and dependent variables $x$ and $y$ do). For a given problem, we usually want to replace parameters with specific values. This is not true of the variables $x$ and $y$.
Slopes of parallel and perpendicular lines
Parallel lines have the same slope
Perpendicular lines have opposite (negative) inverse (reciprocal) slopes
General linear equation
Section 1.8 - Quadratic Functions
Quadratic function
Parabola
Horizontal shifts. Let $c>0$.
$y = f(x+c)$ is a shift to the left.
$y = f(x-c)$ is a shift to the right.
Vertical shifts. Let $c>0$.
$y = f(x) + c$ is a shift up.
$y = f(x) - c$ is a shift down.
Graph of $y=\color{red}{a}x^2$
If $a<0$ parabola opens downward
If $a>0$ parabola opens upward
The larger $\vert a\vert$, the steeper the parabola
Standard form: $y=\color{red}{a}(x-\color{red}{x_1})^2 + \color{red}{y_1}$
Quadratic formula: solutions to $ax^2+bx+c=0$ are $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$