Post on 14-Dec-2015
transcript
L2 Graphing Starters
Parabola Drawing Parabola Drawing SolnParabola Equations Parabola Equations SolnCubic Drawing Cubic Drawing SolnCubic Equations Cubic Equations SolnHyperbola Drawing Hyperbola Drawing SolnHyperbola Equations Hyperbola Equations SolnCircles Circles SolnExponential Drawing Exponential Drawing SolnExponential Equations Exponential Equations SolnLog Drawing Log Drawing SolnLog Equations Log Equations SolnsGraph Intersections Graph Intersections SolnsMixed Drawing Mixed Drawing SolnMixed Equations Mixed Equations SolnExcellence A Excellence A Soln 1Excellence B Excellence B Soln 2
Parabola Drawing
32 2 xy
422 2 xy
5243 2 xy
4121 2 xy
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Draw these graphs
1st Slide
Parabola Drawing Soln
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
32 2 xy
422 2 xy
5243 2 xy
4121 2 xy
1st Slide
Parabola Equations
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Write the equations for these graphs
1st Slide
Parabola Equations Soln
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
3221
xxy
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1241 2 xy 21 2 xy
423 2 xy
1st Slide
Cubic Drawing 1st SlideDraw these graphs
23 xxy
213 xxy
42x2
1y 3
212 xxxyy
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Cubic Drawing Soln
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1st SlideDraw these graphs
23 xxy
213 xxy
42x2
1y 3
212 xxxy 21x3xy
Cubic Equations 1st Slide
Write the equations for these graphs
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Cubic Equations Soln 1st Slide
Write the equations for these graphs
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
21421
xxy
22 xxy
213 xxy
1221 3 xy
Hyperbola DrawingDraw these graphs
1st Slide
24
x
y1x
2y
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Hyperbola Drawing Soln
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1st Slide
24
x
y1x
2y
Hyperbola Equations 1st Slide
Write the equations for these graphs
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Hyperbola Equations Soln 1st Slide
Write the equations for these graphs
32
3
x
y21
3
x
y
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Circles 1st SlideDraw these graphs
y
x
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
43 22 yx
92 22 yx Write the equations for these graphs
y
x
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Circles Soln 1st SlideDraw these graphs
y
x
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
2512 22 yx
532 22 yx
43 22 yx
92 22 yx
Exponential Drawing 1st SlideDraw these graphs
23 xy
xy 22
423 xy
12 xyy
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Exponential Drawing Soln 1st Slide
23 xy
xy 22
423 xy
12 xy
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
x22
1y
Exponential EquationsWrite the equations for these graphs
1st Slide
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Exponential Equations SolnWrite the equations for these graphs
1st Slide
54 2 xy
123 xy
250 x.y22 xy
132 xy
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
x25.1y
Log DrawingDraw these graphs
1st Slide
32 xLogy
xLogy 4 2xLogy 2
1xLogy 3 y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Log Drawing SolnDraw these graphs
1st Slide
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
3xLogy 2
xLogy 4
1xLogy 3
2xLogy 2
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Log EquationsWrite the equations for these graphs
1st Slide
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Log Equations SolnsWrite the equations for these graphs
1st Slide
2xLogy 6
42xLogy 2
3xLogy 4
4xLogy 3
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Graph Intersections 1st Slide
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
9y2x 22 Find the intersection points between
1xy
Graph Intersections Solns 1st Slide
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
9y2x 22 Find the intersection points between
1xy
1x
2x
01x2x
02xx
04x2x2
95x2x2
91x2x4x4x
91x2x
2
2
2
22
22
0y
3y
Coordinates are (1,0) &(-2,-3)
Mixed Drawing 1st SlideDraw these graphs
3x
4y
1xLogy 2
1x2x2
1y
53y x
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
Mixed Drawing Soln 1st SlideDraw these graphs
3x
4y
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1xLogy 2
y
x
1
1
2
2
3
3
4
4
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
1
1
2
2
3
3
4
4
5
5
6
6
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1x2x2
1y
53y x
Mixed Equations 1st Slide
Write the equations for these graphs
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
Mixed Equations Soln 1st Slide
Write the equations for these graphs
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
y
x
1
1
2
2
3
3
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
– 6
– 6
1
1
2
2
3
3
4
4
5
5
– 1
– 1
– 2
– 2
– 3
– 3
– 4
– 4
– 5
– 5
52y1x 22
12xy 2 x2
3y
2x3xxy
Excellence A 1st Slide
The temperature in a heated glasshouse can be modelled using a hyperbola. The form of the equation is given below.
t = temp in centigrade & h = hours after the heating is turned on 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
t
h
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
1) Find an equation to model the temperature
2) Use your equation to find the temperature after 8 hr
CBh
At
Excellence A Soln 1 1st Slide
The temperature in a heated glasshouse can be modelled using a hyperbola. The form of the equation is given below.
t = temp in centigrade & h = hours after the heating is turned on 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
t
h
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
1) Find an equation to model the temperatureC
BhA
t
Excellence A Soln 2 1st Slide
The temperature in a heated glasshouse can be modelled using a hyperbola. The form of the equation is given below.
t = temp in centigrade & h = hours after the heating is turned on 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
t
h
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
1) Find an equation to model the temperature
2) Use your equation to find the temperature after 8 hr
3
114t
Excellence B 1st Slide
A population of hamsters decreases according to an exponential model. In this form:
P = population & m = months
1) Find an equation to model the population
2) Use your equation to find the population after 7 months
5 10 15 20 50 100 150 200 250
P
m
5
5
10
10
15
15
20
20
50
50
100
100
150
150
200
200
250
250
CBAP m
Excellence B Soln 1 1st Slide
A population of hamsters decreases according to an exponential model.
P = population & m = months
1) Find an equation to model the population
5 10 15 20 50 100 150 200 250
P
m
5
5
10
10
15
15
20
20
50
50
100
100
150
150
200
200
250
250
1008.0120 mP
CBAP m
Excellence B Soln 2 1st Slide
A population of hamsters decreases according to an exponential model.
P = population & m = months
2) Use your equation to find the population after 7 months
5 10 15 20 50 100 150 200 250
P
m
5
5
10
10
15
15
20
20
50
50
100
100
150
150
200
200
250
250 1008.0120 xP
CBAP m