Advanced Math

Practice flashcards covering advanced algebra concepts including absolute value, function transformations, quadratic forms, and Desmos calculator strategies.

Absolute value equations

An equation style where you must split the expression into two cases (positive and negative) and solve both.

Integer constraint strategy

If an expression must equal an integer, every variable inside it must independently be an integer; this is used to bound possible answers via inequalities.

$$f(x+k)$$

A function transformation that shifts the graph horizontally; the shift is to the left if the value inside is $+k$.

Vertex form $a(x-h)^2+k$

A quadratic form where the sign of $a$ indicates whether the parabola opens up $(+)$ or down $(-)$, allowing for the quick ruling out of answer choices.

Desmos variable renaming

A strategy to make expressions compatible with Desmos by changing unknown variables to standard letters (e.g., $w \rightarrow x$) and adding sliders for unknowns.

Converting standard ↔ factored form

A process of distributing to match coefficients and then applying given constraints, such as $a \geq 2$, as an inequality to narrow down valid answer choices.

Minimum/maximum value of the function

To find this in factored form, use $-\frac{b}{2a}$ to find the vertex's x-coordinate and substitute it back into the equation to find the y-value.

Adding rational expressions

A procedure requiring a common denominator before combining numerators; you should never multiply denominators together as a shortcut.

Discriminant/no-numbers $b$-or-$c$ problems

Problems where $c = y$-intercept and $a =$ parabola's direction; the discriminant is used to solve for $b$ when no explicit values are provided.

Pattern recognition/Visualization

The "final boss" move for the hardest questions when algebra and Desmos stall; it involves stepping back to reason how each constant ($a$, $b$, $c$) functions in the equation.