Common Graphs

L2MAEL

---

These are the common graphs that were used in the exam:

• Linear
• Parabola
• Hyperbola (more info later)
• Circle (more info later)

You will use simultaneous equations between a linear line, with parabolas, hyperbolas, or circles to find their intersection points.

---

Hyperbolas:

This is a regular hyperbola ( $y=\frac{a}{x}$ ), where $a=1$ on the image above.

$a$ is the scale factor, and if it goes up, the distance between the hyperbola and the origin $(0,0)$ increases. If $a$ falls below $0$, then the graph is inversed.

Here is the generic hyperbola equation that is translatable:

$y=\frac{a}{x-p}+q$

where $(p,q)$ is the vertex coordinate of the parabola.

However, when translating, you must invert the signs for $p$ (try it yourself online!)

$y=\frac{1}{x-3}+2$

Translated graph with asymptote in blue.

Asymptote = $x=3$, and $y=2$.

---

Circles:

Circles are relatively easier than the hyperbolas. This is their generic equation:

$x^2+y^2=r^2$

$r$, is the radius of the circle.

To make the graph translatable, you replace $x$ with $x-p$, and $y$ with $y-q$.

$(x-p{)}^2+(y-q{)}^2=r^2$

when this form is used, the center will be located at $(p,q)$.

Knowing how these graphs aren’t that important in this standard (it is important in as91257, though), as the main thing is solving simultaneous functions.