Find a and b

[nycmathguy]

David Cohen

 

[MathLover1]

y=ax^2+bx+1

passes through (-1,11) and (3,1)

use given points to make system

if (-1,11)
11=a(-1)^2+b(-1)+1
11-1=a-b
10=a-b........solve for a
a=10+b............eq.1


if (3,1)

1=a(3)^2+b(3)+1
1-1=9a+3b
0=9a+3b........solve for a
9a=-3b
a=-3b/9
a=-b/3............eq.2

from eq.1 and eq.2 we have

10+b=-b/3....solve for b
b/3+b=-10
b/3+3b/3=-10
4b/3=-10
b=-10(3/4)
b=-15/2

go to

a=-b/3............eq.2, substitute b
a=-(-15/2)/3
a=5/2

y=(5/2)x^2-(15/2)x+1

 

[nycmathguy]

y=ax^2+bx+1

passes through (-1,11) and (3,1)

use given points to make system

if (-1,11)
11=a(-1)^2+b(-1)+1
11-1=a-b
10=a-b........solve for a
a=10+b............eq.1


if (3,1)

1=a(3)^2+b(3)+1
1-1=9a+3b
0=9a+3b........solve for a
9a=-3b
a=-3b/9
a=-b/3............eq.2

from eq.1 and eq.2 we have

10+b=-b/3....solve for b
b/3+b=-10
b/3+3b/3=-10
4b/3=-10
b=-10(3/4)
b=-15/2

go to

a=-b/3............eq.2, substitute b
a=-(-15/2)/3
a=5/2

y=(5/2)x^2-(15/2)x+1

Nice work as always. What app did you use to make this graph?

 

[MathLover1]

Nice work as always. What app did you use to make this graph?

algebra.com

 

[nycmathguy]

algebra.com

I don't know how to make graphs using algebra.com.

 

[MathLover1]

I don't know how to make graphs using algebra.com.

it's little bit hard, you need to know some html coding

 

[nycmathguy]

it's little bit hard, you need to know some html coding

Ok. Nevermind.

 

[knoppi]

perhaps try https://www.geogebra.org/calculator?

 

[nycmathguy]

perhaps try https://www.geogebra.org/calculator?
View attachment 1159

Cool. Thanks.