This be my Algebra 2 Final Keynote.

Read and be afraid, no?

Tuesday, June 7, 2011

y=2x+0

So you have a line..

You’re given two points. You know the line is linear (doesn’t bend).

Ex: (1, 2)(2,4)

First of all, the equation for a line isy=mx+b

Slope y-intercept

Plug your two points in a rise/run (or y2-y1/x2-x1) equation to find slope.

Ex: y2-y1x2-x1 = 4-2

2-1 =21

For this example,slope = m = 2

Plug in the slope and one x/y coordinate pair to find the y-

intercept.

y=mx+b

2=2(1)+b

b=0

Tuesday, June 7, 2011

Ex: y=4.1258x+313 (x10^4)*

The first number plotted is the

population in 1850. It is the starting point for this line, so it

touches the y-axis.ex: (0, 313)

The next date is 1900. That’s 50 years

after 1850.ex: (50, 513.6)

*(Everything is 1,000 times larger (10^4))

And so on.

Tuesday, June 7, 2011

Population chart

Pair of coordinates.

Finding the slope.Scatter-plot graph.

y-y1=m(x-x1) form

Equation: y=41258.333x+3130000Prediction: 11, 794, 250

Tuesday, June 7, 2011

So you have a quadratic line..

You’re given three points.ex: (0,6) (10,9) (20,15)

The formula is y=ax^2+bx+c

We plug in the first point first, because of the x being 0.

(6)=a(0)^2 + b(0) + c6 = c

Second point:9=a(10)^2 + b(10) + 63=100a+10b

Third Point:15=a(20)^2+b(20)+6

9=400a^2+20bb=(3/10)-10a 9=400a+20([3/10]-10a)

a=.0153=100(.015)+10bb=.15 y=.015x^2+.15x+6

Tuesday, June 7, 2011

The first number plotted is the

population in 1850. Plugging in 0 for x makes y=6. So this line touches the y-

axis at 6.ex: (0,6)

The next date is 1900. That’s 50 years

after 1850.ex: (50, 51)

..And so on.

Example quadratic line isy = 0.015x^2 + 0.15x + 6

Tuesday, June 7, 2011

From three points to an equation...

(0,31) & (140,83) & (150,88) y=ax^2+bx+c

Point One:31=a(0)^2+b(0)+c

c=31

Point Two:83=a(140)^2 +b(140)+3152=19600a +140b

Point Three:88=a(150)^2+b(150)+c57=22500a+150b

150b=-22500a+57b=-150a+(57/150)

52=19600a+140(-150a+[57/150])

52=19600a-2100a+53.2-1.2=-1400a

a=.000857142857143

b=-150(.000857142857143)+(57/150)

b=.251428571428571

Tuesday, June 7, 2011

Equation:

y=(.000857142857143)x^2+(.251428571428571)x+31

Prediction:

x=210y=(.000857142857143)(210)^2+(.251428571428571)(210)+31

y=37.8+52.79999999999991+31y=121.6

Prediction: 121.6 (x104)

Tuesday, June 7, 2011

So you have an exponential curves line..

The formula is y=abx

You’re given two points.(6,7)(8,10)

Ex:

Plug both points in and then substitute.

(7)=ab(6) (10)=ab(8)

a=(7/b6)10=(7/b6)(b8)

10=7b2

b=1.195Plug b in to find a.

a=(7/[1.195]6)a=3.193 ..and you have your equation.

y=(3.193)(1.195)x

Tuesday, June 7, 2011

Example exponential curves line isy=(32.166214450324878)

(1.007725795242675)x

The first number plotted is the

population in 1850. By plugging in 0 for x, b becomes 1, so

y=a.ex: (0, 32.166)

The next date is 1900. That’s 50 years

after 1850.ex: (50, 47.263)

..and so on.

Tuesday, June 7, 2011

From two points to an equation..

(110, 75) & (120, 81) y=abx

Point One:75=ab110

Point One:81=ab120

a=(75/b110) a=(81/b120)

75b110 =

81b120

81=75b10

b=1.007725795242675

75=a(1.007725795242675)110

75=2.331638997054641aa=32.166214450324878

Equation: y=(32.166214450324878)(1.007725795242675)x

Prediction: (210, 161.919374795460997)Tuesday, June 7, 2011

Why is each prediction different?

The first equation is linear,

y=mx+b.The second equation is quadratic,

y=ax2+bx+c

The third equation is exponential,

y=abxThree different formulas, three different lines, three

different predictions.Tuesday, June 7, 2011

Thanks for watching!

Tuesday, June 7, 2011