A 'Graph Plotter' challenge — enter each clue on the same graph and watch the famous apple appear!
How it works: open the Graph Plotter (Desmos graphing calculator) and set your window to \(-12 \le x \le 12\) and \(-12 \le y \le 12\). Work through the clues in order — later shapes are drawn on top of earlier ones.
Restrictions: curly brackets limit how much of a graph
is drawn. For example y=2 {1<x<5} draws the line \(y=2\) only
between \(x=1\) and \(x=5\).
Shading: swap \(=\) for \(\le\) to fill a shape in.
The badge is a ring between two circles, both centred at the origin: one with radius \(8\) and one with radius \(10\).
A circle centred at the origin has equation \(x^2+y^2=r^2\). To shade only the ring, fill the inside of the big circle, but add a restriction in curly brackets that keeps you outside the small one:
\(x^2+y^2 \le 10^2\;\{x^2+y^2 \ge 8^2\}\)
Colour it golden yellow (clue 8).
The apple is a squashed circle (an ellipse), centred at the origin, \(14\) units wide and \(12\) units tall. An ellipse like this has equation
\(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2} \le 1\)
where \(a\) is half the width and \(b\) is half the height. Work out \(a\) and \(b\), then shade it red.
Each eye is a small white ellipse, \(2\) units wide and \(3\) units tall. The left eye is centred at \((-2,\,2)\):
\((x+2)^2+\left(\dfrac{y-2}{1.5}\right)^2 \le 1\)
Now write the equation of the right eye, which is the mirror image in the \(y\)-axis.
Plot a point for each pupil: \((x + 1.5)^2 + (y - 1.5)^2 \le 0.45^2\) and \((x - 2.5)^2 + (y - 1.5)^2 \le 0.45^2\). Long-press the colour icon to make them black and drag the point size up to large.
The open mouth is the region trapped between a parabola and a horizontal line:
Shade between them by typing the compound inequality \(0.3x^2-5.2 \le y \le -2.5\), coloured white. Then add the bottom-lip parabola again on its own, restricted so it only spans the mouth, as a bold black curve.
The stem is a slanted quadrilateral. Use the polygon command
with these vertices in order, and colour it brown:
\((-0.5,\,5.5),\;(1,\,5.5),\;(1.5,\,8.5),\;(0,\,8.5)\)
The leaf is a green ellipse centred at \((-3,\,8.5)\), \(5\) units wide and \(3\) units tall:
\(\left(\dfrac{x+3}{2.5}\right)^2+\left(\dfrac{y-8.5}{1.5}\right)^2 \le 1\)
Add the vein down the middle: a straight line with gradient \(0.2\) passing through the centre of the leaf, drawn only for \(-5<x<-1\). Use the form \(y-y_1=m(x-x_1)\).
Define these custom colours, then long-press the colour icon of each expression and pick them from the swatches:
