Posted by Ashley on Thursday, February 24, 2011 at 9:42pm.
y= ax^2+bx4. How would i find the equation of this parabola with the points (0,4) (1,0) (2,2) (4,0) and 6,10)?

Math (Help This Will Be on My Test Tomorrow!)  Reiny, Thursday, February 24, 2011 at 10:43pm
Use the first few given points
for (0,4) : 4 = 0 + 0  4 , nothing new learned here
for (1,0) : 0 = a + b  4 > a+b+4 or b = 4a
for (2,2) : 2 = 4a + 2b  4  2a + b = 3
use substitution
2a + (4a) = 3
a = 1
then b = 4(=1) = 5
y = x^2 + 5x  4
test if the other points satisfy, they do!

Math (Help This Will Be on My Test Tomorrow!)  Bosnian, Thursday, February 24, 2011 at 10:53pm
You must write equation for any pair of points.
y=ax^2+bx4
x=0 y= 4
4=a*0^2+b*0+c
0+0+c= 4
c= 4
x=1 y=0
0=a*1^2+b*14
a*1+b*14=0
a+b4=0
a=4b
x=2 y=2
y=ax^2+bx4
2=(4b)*2^2+b*24
(4b)*4+2b4=2
164b+2b=2+4
2b=616
2b= 1 Divide with 2
b=5
a=4b
a=45
a= 1
So:
a= 1 b=5 c= 4
y=ax^2+bx+c= x^2+5x4
y=x^2+5x4
Checking of results:
For x=4
y=ax^2+bx4
y= 4^2+5*44
y= 16+204
y=44
y=0
Correct value
For x=6
y=ax^2+bx4
y= 6^2+6*54
y= 36+304
y= 64
y= 10
Correct value

Math (Help This Will Be on My Test Tomorrow!)  Bosnian, Thursday, February 24, 2011 at 10:55pm
I make one mistake in typig.
2b= 1 Divide with 2 is mistake
2b= 10 Divide with 2 is correct
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