Geometry and Functions Flashcards

Vocabulary flashcards based on the mathematical descriptions of a parabola, a line, and the geometric construction of triangles from their points.

Parabola $p$

The parabola defined by the equation $y = \frac{2}{3}(x-3)^2 - 3$ with $G = \mathbb{R} \times \mathbb{R}$.

Straight Line $g$

The line defined by the equation $y = -x + 0.5$ with $G = \mathbb{R} \times \mathbb{R}$.

Points $A_n$

Points located on the parabola $p$ with coordinates $(x \mid \frac{2}{3}(x-3)^2 - 3)$.

Points $C_n$

Points located on the straight line $g$ with coordinates $(x \mid -x + 0.5)$ that share the same abscissa $x$ as points $A_n$.

Vector $\vec{A_n B_n}$

The translation vector used to define the position of points $B_n$ relative to $A_n$, given as $\vec{A_n B_n} = \begin{pmatrix} 3 \\ 1 \end{pmatrix}$.

Triangle Existence Interval

The range of $x$ values for which the points $A_n$, $B_n$, and $C_n$ form the vertices of a triangle: $x \in ]0.28; 7.05[$.

Abscissa $x$

The horizontal coordinate shared by points $A_n$ and $C_n$, which determines their vertical positions on the parabola $p$ and line $g$ respectively.