MYP Standard Mathematics Functions and Quadratic Relationships Key Definitions

The vertical line that divides the parabola into two mirror-image halves. Its equation is $x=x_v$.

A method of rewriting a quadratic into a perfect-square form (plus or minus a constant), allowing solutions by taking square roots.

The value $\Delta=b^2-4ac$ for $ax^2+bx+c=0$, which determines the number of real solutions.

The set of all input values $x$ used in a relation or function.

A relation in which every input value in the domain is mapped to one and only one output value in the range.

A relation where at least one input maps to multiple outputs and at least one output is shared by multiple inputs.

A relation where two or more different inputs are mapped to the same output.

A relation where at least one input is mapped to more than one output.

A relation where each input is mapped to a unique output, and no two different inputs share the same output.

An equation that can be written in the form $ax^2+bx+c=0$ where $a\neq 0$.

An algebraic expression in one variable whose highest exponent is 2 (and with a non-zero $x^2$ term). It can be written in the form $ax^2+bx+c$ where $a\neq 0$.

A function whose graph is a parabola and can be written in the form $y=ax^2+bx+c$ where $a\neq 0$.

The set of all possible output values (often $y$-values) that the function can produce from its set of input values (the domain).

A set of ordered pairs $\{(x,y)\}$ that links elements from one set (inputs) to elements of another set (outputs).

A zero where the factor repeats, for example $(x-h)^2$. The graph touches the x-axis at $x=h$ but does not cross it.

The turning point of the parabola, with coordinates $(x_v, y_v)$.

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

The $x$-coordinates where the graph crosses the $x$-axis (where $y=0$). They are also called the zeros (or roots) of the function.

The point where the graph crosses the $y$-axis (where $x=0$).